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Students can Download Chapter 5 Law of Motion Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 5 Law of Motion

Summary
Introduction
In this chapter we are going to learn about the laws that governs the motion of bodies.
Inertia:
The inability of a body to change by itself it’s state of rest or uniform motion along a straight line is called inertia.
Examples of inertia:
1. When a fast moving bus is suddenly stopped, a standing passenger tends to fall in the forward direction.
Explanation
The passenger has the same velocity as that of the bus. When the bus stops suddenly the lower part of his body is brought to rest suddenly because of the friction between his feet and floor of the bus. But the upper part continues to move because of its inertia.

2. When a bus suddenly takes off, a standing passenger tends to fall in the backward direction. This is because the lower part of the body gets a speed when the bus picks up speed and upper part continues to be at rest because of its inertia.

3. Consider a person sitting inside a stationary train and tossing a coin. The coin falls into his own hand. If he repeats the experiment when the train is moving with uniform speed, then also the coin falls into his own hand.

4. Cleaning a carpet by beating is in accordance with law of inertia.

5. Rabbit chased by a dog runs in zigzag manner. This is to take advantage of the large inertia of the massive dog.

6. A person chased by an elephant runs in a zigzag manner or in a circle. This is to take the advantage of the large inertia of the massive elephant.

Newton’s Laws:
Newton built on Galileo’s ideas and laid the foundation of mechanics in terms of three laws.

• Newtons first law
• Newtons second law
• Newtons third law

Newton’s First Law Of Motion
Everybody continues in its state of rest or of uniform motion along a straight line unless it is compelled by an external unbalanced force to change that state:
Note: Newton’s first law of motion brings the idea of inertia. Inertia of a body is measured by the mass of the body. Heavier the body, greater is the force required to change its state and hence greater is its inertia.

Newton’s Second Law Of Motion
Linear Momentum (\(\vec{p}\)):
Momentum of a body is defined as the product of its mass m and velocity \(\vec{v}\)

Explanation
Momentum of a body can be produced or destroyed by the application of force on it. Therefore, momentum of a body is measured by the force required to stop the body in unit time.
Force required to stop a moving body depends upon

1. mass of the body
2. velocity of the body.

1. Mass of the body:
When a ball and a big stone are allowed to fall from the same height, we find that a greater force is required to stop the big piece of stone than the ball. Thus larger the mass of a body, greater is its linear momentum.

2. Velocity of the body:
A bullet thrown with the hand can be stopped easily than the same bullet fired from the gun. Therefore, langerthe velocity of a body, greater is its linear momentum.
Note: Momentum is a vector quantity. Its unit is Kgms^-1
Newton’s Second Law of motion:
The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. Mathematically this can be written as

Question 1.
Derive F = ma from Newton’s Second law.
Answer:
Consider a body of mass ‘m’ moving with a momentum \(\vec{p}\). Let \(\vec{F}\) be the force acting on it for time internal Dt. Due to this force the momentum is changed from \(\vec{p}\) to p + Dp. Then according to Newtons second law, we can write

Where K is a constant proportionality. When we take the limit ∆t → 0, we can write

Unit of force:
Unit of force is newton. 1N = 1Kgms^-2
Force in terms of the components:
We know force is a vector, Hence we can write as


Impulsive force:
The forces which act on bodies for short time are called impulsive forces.
Example:

• In hitting a ball with a bat
• In firing a gun

Impulse:
An impulse force does not remain constant, but changes from zero to maximum. This impulsive force is not easy to measure, because it changes with time. In such a case, we measure the total effect of the force called impulse.

The impulse of a force is the product of the average force and the time for which it acts.

Relation between impulse and momentum:
We know from Newtons second law
F = \(\frac{\Delta p}{\Delta t}\)

R.H.S. is the impulse and L.H.S. is change of momentum ie; change of momentum = impulse.

Question 2.
When we jump to hard soil there is greater discomfort than when we jump to loose soil. Why?
Answer:
F = \(\frac{\Delta p}{\Delta t}\). When we jump to hard soil, Dt is small and F is large. When we jump to loose soil it takes more time for the body to come to rest. Therefore, Dt is large and F will be small.

Question 3.
A cricketer draws his hand while catching a cricket ball. Why?
Answer:
When cricketer draws his hand, the Dt will increase. Hence F acting on the hand will decrease.

Newtons Third Law Of Motion
Statement:
To every action, there is always an equal and opposite reaction.
Explanation: When a book is placed on the table, the weight of the book acts on the table downwards. The table exerts an equal force on the book in the upward direction. If the force applied by the book on the table is action, the force applied by the table on the book is reaction.

Question 4.
If action and reaction are equal and opposite, why they do not cancel?
Answer:
Though action and reaction are equal and opposite, they do not cancel each other because action is on one body and reaction is on another body.
Consider a pair of bodies A and B. According to the
third law F_AB = – F_BA
(force on A by B) = – (force on B by A).

Conservation Of Momentum
Second law and third law lead to conservation of linear momentum.
Statement:
When there is no external force on a body (or system), the total momentum remains constant.

Proof in the case of a single body:
According to Newtons second law, F = \(\frac{d p}{d t}\). if F = 0, we get p = constant. Which means that momentum of a body remains constant, if there is no external force acting on it.

Conservation of momentum in the case of firing a gun:
Consider a gun of mass M and bullet of mass ‘m’ at rest. On firing the gun exerts a force F on the bullet and bullet exerts an equal force -F in the opposite direction. Because of this action and reaction (due to firing), the gun acquires a momentum P_g and bullet acquires a momentum P_b.
Momentum before firing
The bullet and gun are at rest. Hence momentum before firing = M × 0 + m × 0
Momentum before firing = 0 ________(1)
Momentum after firing
According to Newtons second law, the change in
momentum of bullet. ∆P_b = P_b – 0 = F∆t ______(2)
Since initially both are rest,
Dp = final momentum – initial
momentum Similarly the change in momentum of gun
∆p_g = p_g – 0 = -F∆t _______(3)
∴ Total momentum after firing = p_b + p_g
= F∆t + – F∆t.
Total momentum after firing = 0 _______(4)
from eq (1) and eq (4), we get,
Total momentum before firing = Total momentum after firing.

Conservation of momentum in the case of two colliding bodies:

Consider two bodies A and B with initial momenta P_A and P_B. After collision, they acquire momenta P¹_A and P¹_g respectively.
According to Newton’s second law, the change in momentum of A due to the collision with B,

Similarly the change in momentum of B due to the collision with A, F_BA∆t = P¹_B – P_B

[Where Dt is time for which the two bodies are in contact].
According Newton’s third law, we can write
F_AB = -F_BA

Total momentum before collision = Total momentum after collision.
Note: Conservation linear momentum is always satisfied for elastic collision and inelastic collision.

Equilibrium Of A Particle
Equilibrium of a particle in mechanics refers to the situation, when the net external force on the particle is zero.

Common Forces In Mechanics
There are two types of forces commonly used in mechanics,

1. Contact forces
2. Non contact forces

1. Contact forces:
A contact force on an object arises due to contact with some other object. Example : Friction, viscosity, air resistance etc.

2. Non contact forces:
A non contact force on an object arises due to non contact with some other object
Example: Gravitational force

Friction:
Friction is the force that develops at the surfaces of contact of two bodies and impedes (opposes) their relative motion.
There are different types of friction.

• Static friction: The opposing force that comes into play when one body tends to move over the surface of another (but the actual motion has yet not started)
• Limiting friction (f_s): The maximum value of static friction is called limiting friction.
• Kinetic friction (f_k)(or) dynamic friction: Kinetic friction or dynamic friction is the opposing force that comes into play when one body is actually moving’overthe surface of another body.
• Sliding friction: The opposing force that comes into play when one body is actually sliding over the surface of the other body is called sliding friction.
• Rolling friction: The opposing force that comes into play when one body is actually rolling over the surface of the other body is called rolling friction.

Laws of static Friction:

• The force of maximum static friction is directly proportional to the normal reaction
• The force of static friction is opposite to the direction in which the body tends to move.
• The force of static friction is parallel to the surfaces in contact.
• The force of maximum static friction is independent of the area of contact (as long as the normal reaction remains constant).
• The force of static friction depends only on the nature of surfaces in contact.

a. Laws of Kinetic friction:

1. The force of Kinetic friction is proportional to normal reaction.
2. The force of Kinetic friction is opposite to the dh rection in which the body moves.
3. The force of Kinetic friction is parallel to the surfaces in contact.
4. The force of Kinetic friction is independent of the area contact (as long as the normal reaction remains constant)
5. The force of Kinetic friction depends on the nature of surface.
6. Force of Kinetic friction is almost independent of the speed.
7. Force of Kinetic friction is less than force of static friction.

b. Coefficient of static friction:
The force of static friction (f_s)_max is directly proportional to the normal reaction N
(f_s)_max α N

Where m_s is called coefficient of static friction.
Definition of m_s
Coefficient of static friction is the ratio of the force of the maximum static friction to the nprmal reaction.

c. Coefficient of Kinetic friction:
The force of kinetic friction is directly proportional to the normal reaction N.
i e (f_k)_max α N

Where µ_k is called coefficient of Kinetic friction.
Definition of µ_k
Coefficient of Kinetic friction is the ratio of the force of Kinetic friction to the normal reaction.

d. Angle of friction:
Angle of friction is the angle whose tangent gives the coefficient of friction.

Proof:
Consider a body placed on a surface. Let N be the normal reaction and f_limit is the limiting friction. Let ‘θ’ be the angle between Resultant vector and normal reaction. From the triangle OBC,

∴ tanθ = µ
Angle of repose:
The angle of repose is the angle of the inclined plane at which a body placed of it just begins to slide.
Explanation
considers body placed on a inclined plane. Gradually increase the angle of inclination till the body placed on its surface just begins to slide down. If α is the inclination at which the body just begins to slide down, then α is called angle of repose.

The limiting friction F acts in upward direction along the inclined plane. When the body just begins to move, we can write
F = mg sin α ______(1)
from the figure normal reaction,
N = mg cos α ______(2)
dividing eq (1) by eq (2)

Note: Angle of repose is equal to angle of friction.
Rolling friction:
Why rolling friction is less than kinetic friction?
When a body rolls over a plane, there is just one point of contact between the body and plane. The relative motion between point and plane is zero. Hence in this ideal situation, kinetic friction becomes zero.
Advantages of friction

• Friction helps us to walk on the ground.
• Friction helps us to hold objects.
• Friction helps in striking matches.
• Friction helps in driving automobiles.
• Friction is helpful in stopping a vehicle etc.

Disadvantages of friction

• Friction produces wear and tear.
• Friction leads to wastage of energy in the form of heat.
• Friction reduces the efficiency of the engine etc.

Steps to reduce friction

• Polishing the surfaces in contact
• Use of lubricants
• Ball bearing placed between moving parts of machine.

Circular Motion
When a body moves along circumstances of a circle, there is an acceleration towards it’s centre. This acceleration is called centripetal acceleration. The force providing this acceleration is called centripetal force.
Centripetal force f = \(\frac{\mathrm{mv}^{2}}{\mathrm{R}}\)

1. For a stone rotated in a circle by a string, the centripetal force is provided by the tension in the string.
2. The centripetal force for motion of a planet around the sun is the gravitational force on the planet due to sun.
3. For a car on circular road, the centripetal force is provided by the friction between tire and road.

1. Motion of a car on a level road:

Consider a vehicle moving overa level curved road. The two forces acting on it are

• Weight (mg) vertically down
• The reaction (N)

The normal reaction can’t produce sufficient centripetal force required for circular motion. The centripetal force for circular motion is provided by friction. This friction opposes the motion of the car moving away from the circular road. Hence condition for circular motion can be written as Centripetal force ≤ force of friction

The maximum speed of circular motion of the car
v_max = \(\sqrt{\mu_{s} \mathrm{rg}}\)

Question 5.
Why surface of the road is kept inclined to the horizontal?
Answer:
Consider a vehicle moving along a level curved road. The vehicle will have a tendency to slip outward. This outward slip is prevented by frictional force. But friction causes unnecessary wear and tear. More over, for typical value of µ and R the maximum speed v = \(\sqrt{\mu_{s} \mathrm{rg}}\) rg will be very small.

These defects can be avoided if we raise the outer edge of the road slightly above the inner edge. This process is called banking of curve. The angle made by the surface of the road with the horizontal is called the angle of banking.

2. Motion of a car on a banked road:


Consider a vehicle along a curved road with angle of banking q. Then the normal reaction on the ground will be inclined at an angle q with the vertical.

The vertical component can be divided into N Cosq (vertical component) and N sinq (horizontal component). Suppose the vehicle has a tendency to slip outward. Then the frictional force will be developed along the plane of road as shown in the figure. The frictional force can be divided into two components. Fcosq (horizontal component) and F sinq (vertical component).
From the figure are get
N cos q = F sinq + mg
N cosq – F sinq = mg ______(1)
The component Nsinq and Fsinq provide centripetal force. Hence

Dividing both numerator and denominator of L.H.S by N cosq. We get

This is the maximum speed at which vehicle can move over a banked curved road.

Optimum speed:
Optimum speed is the speed at which a vehicle can move over a curved banked road without using unnecessary friction.
When a car is moved with optimum speed V_o, m can be taken as zero.
putting m = 0 in the above equation we get

Students can Download Chapter 2 Forms of Business Organisation Notes, Plus One Business Studies Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Business Studies Notes Chapter 2 Forms of Business Organisation

Contets

• Sole Proprietorship – Meaning – Features Advantages & Disadvantages
• Joint Hindu Family Business (H.U.F) – Meaning – Features – Advantages & Disadvantages
• Partnership – Meaning – Features – Advantages & Disadvantages – Types of Partners – Types of Partnership – Partnership Deed – Registration
• Co operative Society – Meaning – Features Advantages & Disadvantages – Types of Co-operative Societies
• Joint Stock Company- Meaning – Features – Advantages & Disadvantages – Types of Companies-Choice of form of Business organisation

Various forms of business organisations are:

(a) Sole proprietorship,
(b) Joint Hindu family business,
(c) Partnership,
(d) Cooperative societies, and
(e) Joint stock company.

Sole proprietorship:
Sole proprietorship refers to a form of business organization which is owned, managed and controlled by an individual who is the recipient of all profits and bearer of all risks. It is the most common form of business organization.
Features:

1. The sole trader is the single owner and manager of the business.
2. The formation of a sole proprietorship is very easy. There are no legal formalities to form and close a sole proprietorship.
3. The liability of a sole trader is unlimited, i.e. in case of loss, his personal properties can be used to pay the business liabilities.
4. The entire profit of the sole trading business goes to the sole proprietor. If there is any loss it is also to be borne by the sole proprietor alone.
5. The sole trader has full control over the affairs of the business. So he can take quick decisions.
6. A sole trading concern has no legal existence separate from its owner.
7. The death, insolvency etc. of a sole trader causes discontinuity of business.

Merits:
1. Easy formation:
The formation of a sole proprietorship is very easy. There are no legal formalities to form and close a sole proprietorship.

2. Quick Decision:

The sole trader has full control over the affairs of the business. So he can take quick decisions and prompt actions in all business matters.

3. Motivation:
The entire profit of the sole trading business goes to the sole proprietor. It motivates him to work hard.

4. Secrecy:
A sole trader can keep all the information related to business operations and he is not bound to publish firm’s accounts.

5. Close Personal Relation:

The sole proprietor can maintain good personal contact with the customers and employees and thus, business runs smoothly.

Limitations

1. Limited capital: A sole trader can start business only on a small scale because of limited capital.
2. Lack of Continuity: Death, insolvency or illness of a proprietor affects the business and can lead to its closure.
3. Limited managerial ability: A sole proprietor may not be an expert in every aspect of management.
4. Unlimited liability: The liability of a sole trader is unlimited, i.e. in case of loss, his personal properties can be used to pay off the business liabilities.
5. Suitability: Sole proprietorship is suitable in the following cases.
   • Where the market is limited, localized and customers demand personalized services. Eg. tailoring, beauty parlour etc.
   • Where goods are unstandardized like artistic jewellery.
   • Where lower capital, limited risk & limited managerial skills are required as in case of retail store.

Joint Hindu Family Business (HUF):
It refers to a form of organisation where in the business is owned and carried on by the members of a joint Hindu family. It is also known as Hindu Undivided Family Business (H.U.F). It is governed by Hindu succession Act, 1956. It is found only in India.

The business is controlled by the head of the family who is the eldest member and is called karta. All members have equal ownership right over the property of an ancestor and they are known as co-parceners.

Features
1. Formation:
For a Joint Hindu family business there should be at least two members in the family and some ancestral property to be inherited by them.

2. Membership:

Membership by virtue of birth in the family.

3. Liability:
The Karta has unlimited liability. Every other coparcener has a limited liability up to his share in the HUF property.

4. Control:
The control of the family business lies with the karta. He takes all the decisions and is authorised to manage the business.

5. Continuity:

The business is not affected by the death of the Karta as in such cases the next senior male member becomes the Karta.

6. Minor Members:
The basis of membership in the business is birth in the family. Hence, minors can also be members of the business.

Merits
1. Effective control:
The karta has absolute decision making power. This avoids conflicts among members

2. Continuity of business:
The death of the karta will not affect the business as the next eldest member will then take up the position

3. Limited liability of members:
The liability of all the co-parceners except the karta is limited to their share in the business.

4. Increased loyalty:
Members are likely to work with dedication, loyalty and care, because the work involves the family name.

Limitation
1. Limited capital:
The capital of HUF is limited since the ancestral property only can be used for the business. This reduces the scope for business growth.

2. Unlimited liability:
The liability of Karta is unlimited. His personal property can be used to repay business debts.

3. Dominance of karta:
There is a possibility of differences of opinion among the members of the Joint Family. It may affect the stability of the business.

4. Limited managerial skills:
The karta may not be an expert in all areas of management. It may affect the profitability of the business.

Partnership:
The Indian Partnership Act, 1932 defines partnership as “the relation between persons who have agreed to share the profit of the business carried on by all or any one of them acting for all.”
Features

1. Formation: For the formation of a partnership, agreement between partners is essential.
2. Liability: The partners of a firm have unlimited liability. The partners are jointly and individually liable for payment of debts.
3. Risk bearing: The profit or loss shall be shared among the partners equally or in agreed ratio.
4. Decision making and control: The activities of a partnership firm are managed through the joint efforts of all the partners.
5. Lack of Continuity: The retirement, death, insolvency, insanity etc of any partner brings the firm to an end.
6. Membership: There must be at least two persons to form a partnership. The maximum number of persons is ten in banking business and twenty in non banking business.
7. Mutual agency: In partnership, every partner is both an agent and a principal.

Merits of Partnership:

1. Easy formation and closure:
A partnership firm can be formed and closed easily without any legal formalities.

2. Balanced decision making:
In partnership, decisions are taken by all partners. So they can take better decisions regarding their business.

3. Division of labour:
Division of labour is possible in partnership firm. Duties can be assigned to different partners according to their ability.

4. Large funds:
In a partnership, the capital is contributed by a number of partners. So they can start business on a large scale.

5. Sharing of risk:
The risks involved in running a partnership firm are shared by all the partners. This reduces the anxiety, burden and stress on individual partners..

6. Secrecy:
A partnership firm is not legally required to publish its accounts and submit its reports. Hence it can maintain confidentiality of information relating to its operations.

Limitations of Partnership:
1. Unlimited liability:
The partners of a firm have unlimited liability. The partners are jointly and individually liable for payment of debts.

2. Limited resources:
There is a restriction on the number of partners. Hence capital contributed by them is also limited.

3. Possibility of conflicts:
Lack of mutual understanding and co-operation among partners may affect the smooth working of the partnership business.

4. Lack of continuity:
The retirement, death, insolvency, insanity etc of any partner brings the firm to an end.

5. Lack of public confidence:
A partnership firm is not legally required to publish its financial reports. As a result, the confidence of the public in partnership firms is generally low.

Types of Partners:
1. Active partner:
A partner who contribute capital and takes active part in the business is called an active partner.

2. Sleeping (Dormant partner):
Partners who do not take part in the day to day activities of the business are called sleeping partners. He contributes capital, share profits and losses and has unlimited liability.

3. Secret partner:
A secret partner is one whose association with the firm is unknown to the general public. He contributes to the capital, takes part in the management, shares its profits and losses, and has unlimited liability.

4. Nominal partner (Quasi Partner):
A nominal partner neither contributes capital nor takes any active part in the management of the business. He simply lend his name to the firm. But, he is liable to third parties for all the debts of the firm.

5. Partner by estoppel:
If a partner by his talk or action leads others to believe that he is a partner in a firm, then he is known as partner by estoppel. However, he is liable to third parties.

6. Partner by holding out:
if a partner declares that a particular person is a partner of their firm, and such a person does not disclaim it, then he/she is known as ‘Partner by Holding out’. Such partners are not entitled to profits but are liable to third parties.

7. Minor Partner:
A minor can be admitted to the benefits of a partnership firm with the mutual consent of all other partners. In such cases, his liability will be limited to the extent of the capital contributed by him.

He will not be eligible to take an active part in the management of the firm. But, a minor can share only the profits and cannot be asked to bear the losses. However, he can inspect the accounts of the firm.

Types of Partnerships:
On the basis of duration, there are two types of partnerships:

1. Partnership at will
2. Particular partnership

1. Partnership at will:
This type of partnership exists at the will of the partners. It can continue as long as the partners want and is terminated when any partner gives a notice of withdrawal from partnership to the firm.

2. Particular partnership:
Partnership formed for the accomplishment of a particular project or for a specified time period is called particular partnership.

On the basis of liability, the two types of partnerships are:

1. General partnership
2. Limited partnership

1. General Partnership:
In general partnership, the liability of partners is joint and unlimited. Registration of the firm is optional. The existence of the firm is affected by the death, lunacy, insolvency or retirement of the partners.

2. Limited Partnership:
In limited partnership, the liability of at least one partner is unlimited whereas the rest may have limited liability. Registration of such partnership is compulsory. Such a partnership does not get terminated with the death, lunacy or insolvency of the limited partners. This form of partnership is permitted in India after the introduction of Small Enterprise Policy in 1991.

Partnership Deed:
The written agreement which specifies the terms and conditions that govern the partnership is called the partnership deed;
Contents

1. Name of firm
2. Nature of business and location of business
3. Duration of business
4. Investment made by each partner
5. Profit sharing ratio
6. Rights, duties and powers of the partners
7. Salaries and withdrawals of the partners
8. Terms governing admission, retirement and expulsion of a partner
9. Interest on capital and interest on drawings
10. Procedure for dissolution of the firm
11. Preparation of accounts and their auditing
12. Method of solving disputes

Registration of partnership:
According to Indian Partnership Act 1932, registration of a partnership is not compulsory, it is optional. However, they can register with the Registrar of firms of the state in which the firm is situated.
Procedure for Registration:

1. 1. Submission of application in the prescribed form to the Registrar of firms. The application should contain the following particulars:
   • Name of the firm
   • Location of the firm
   • Names of other places where the firm carries on business
   • The date when each partner joined the firm
   • Names and addresses of the partners
   • Duration of partnership. This application should be signed by all the partners.
2. Deposit of required fees with the Registrar of Firms.
3. The Registrar after approval will make an entry in the register of firms and will subsequently issue a certificate of registration. The consequences of non-registration of a firm are as follows:
   • A partner of an unregistered firm cannot file suit against the firm or other partner.
   • The firm cannot file a suit against third party.
   • The firm cannot file a case against its partner.

Co-operative Society:
The cooperative society is a voluntary association of persons, who join together with the motive of welfare of the members. The basis of co-operation is self help through mutual help, the motto is “each for all and all for each”.

The cooperative society is compulsorily required to be registered under the Cooperative Societies Act 1912. At least ten persons are required to form a society. The capital of a society is raised from its members through issue of shares.

Features:
The important features of a co-operative society are:

1. Voluntary membership: The membership of a cooperative society is voluntary. Membership is open to all, irrespective of their religion, caste, and gender.
2. Legal status: Registration of a cooperative society is compulsory.
3. Limited liability: The liability of the members of a cooperative society is limited to the extent of the amount contributed by them as capital.
4. Control: Management and control lies with the managing committee elected by the members.
5. Service motive: ‘Self help through mutual help’ or ‘each for all and’ all for each’ is the foundation of co-operative society.

Merits:

1. Equality in voting status: The principle of ‘one man one vote’governs the cooperative society.
2. Limited liability: The liability of members of a cooperative society is limited to the extent of their capital contribution.
3. Stable existence: Death, insolvency or insanity of the members do not affect continuity of a cooperative society.
4. Economy in operations: Co-operative society aims to eliminate middlemen. This helps in reducing cost.
5. Support from government: A co-operative society gets support from the government in the form of low taxes, subsidies and low interest rates on loans.
6. Easy formation: The cooperative society can be started with a minimum often members. Its registration procedure is simple involving a few legal formalities

Limitations:

1. Limited resources:
Resources of a cooperative society consists of limited capital contributions of the members.

2. Inefficiency in management:
Cooperative societies are unable to attract and employ expert managers because of their inability to pay them high salaries.

3. Lack of secrecy:
As a result of open discussions in the meetings of members it is difficult to maintain secrecy about the operations of a cooperative society.’

4. Government control:
cooperative societies have to comply with several rules and regulations related to auditing of accounts, submission of accounts, etc. It affects its freedom of operations.

5. Differences of opinion:
The different viewpoints of members in a co-operative society may lead to difficulties in decision making.

Types of co-operative society:
1. Consumer’s cooperative societies:
The consumer cooperative societies are formed to protect the interests of consumers. The society aims at eliminating middlemen to achieve economy in operations. It purchases goods in bulk directly from the wholesalers and sells goods to the members at the lowest price.

2. Producer’s cooperative societies:
These societies are set up to protect the interest of small producers. It supplies raw materials, equipment and other inputs to the members and also buys their output for sale.

3. Marketing cooperative societies:
Such societies are established to help small producers in selling their Products. It collects the output of individual members and sell them at the best possible price. Profits are distributed to members.

4. Farmer’s cooperative societies:
These societies . are established to protect the interests of farmers by providing better inputs at a reasonable cost. Such societies provide better quality seeds, fertilizers, machinery and other modern techniques for use in the cultivation of crops.

5. Credit cooperative societies:
Credit cooperative societies are established for providing easy credit on reasonable terms to the members. Such societies provide loans to members at low rates of interest.

Joint Stock company:
A company may be defined as a voluntary association of persons having a separate legal entity, with perpetual succession and a common seal. It is an artificial person created by law. The companies in India are governed by the Indian . Companies Act, 1956.

The capital of the company is divided into smaller parts called ‘shares’ which can be transferred freely, (except in a private company). The shareholders are the owners of the company. The company is managed by Board of Directors, elected by shareholders.
Features:
1. Incorporated association:
A company is an incorporated association, i.e. Registration of a company is compulsory under the Indian Companies Act, 1956.

2. Separate legal entity:
A company is an artificial person created by law. Company has a separate legal entity apart from its members. It can enter into contracts, own property, sue and be sued, borrow and lend money etc.

3. Formation:
The formation of a company is a time consuming, expensive and complicated process.

4. Perpetual succession:
A company has a continuous existence. Its existence not affected by death, insolvency or insanity of shareholders. Members may come and go, but the company continues to exist.

5. Control:
The management and control of the affairs of the company is in the hands of Board of directors who are elected the representatives of the shareholders.

6. Liability:
The liability of the shareholders is limited to the extent of the face value of shares held by them.

7. Common seal:
The Company being an artificial person acts through its Board of Directors. All documents issued by the company must be authenticated by the company seal.

8. Transferability of shares:
Shares of a joint stock company are freely transferable except in case of a private company.

Merits:

1. Limited liability:
The liability of the shareholders is limited to the extent of the face value of shares held by them. This reduces the degree of risk borne by an investor.

2. Transferability of shares:
Shares of a public company are freely transferable . It provides liquidity to the investor.z

3. Perpetual existence:
A company has a continuous existence. Its existence not affected by death, insolvency or insanity of shareholders.

4. Scope for expansion:
A company has large financial resources. So it can start business on a large scale.

5. Professional management:
A company can afford to pay higher salaries to specialists and professionals. This leads to greater efficiency in the company’s operations.

6. Public confidence:
A company must publish its audited annual accounts. So it enjoys public confidence.

Limitations:

1. Difficulty in formation:
The formation of a company is very difficult. It requires greater time, effort and extensive knowledge of legal requirements.

2. Lack of secrecy:
It is very difficult to maintain secrecy in case of public company, as company is required to publish its annual accounts and reports.

3. Impersonal work:
It is difficult for the owners and top management to maintain personal contact with the employees, customers and creditors.

4. Numerous regulations:
The functioning of a company is subject to many legal provisions and compulsions. This reduces the freedom of operations of a company.

5 Delay in decision making:
A company takes important decisions by holding company meetings. It requires a lot of time.

6. Oligarchic management:
Theoretically, a company is democratically managed but actually it is managed by few people, i.e board of directors. The Board of Directors enjoy considerable freedom in exercising their power which they sometimes ignore the interest of the shareholders.

7. Conflict in interests:
There may be conflict of interest amongst various stakeholders of a company. It affects the smooth functioning of the company.

8. Lack of motivation:
The company is managed by board of directors. They have little interest to protect the interest of the company.

Types of Companies:
A company can be either a private or a public company.
Private Company:
A private company means a company which:

1. restricts the right of members to transfer its shares
2. has a minimum of 2 and a maximum of 50 members
3. does not invite public to subscribe to its share capital
4. must have a minimum paid up capital of Rs.1 lakh

It is necessary for a private company to use the word private limited after its name.

Privileges of a private company:

1. A private company can be formed by only two members.
2. There is no need to issue a prospectus
3. Allotment of shares can be done without receiving the minimum subscription.
4. A private company can start business as soon . as it receives the certificate of incorporation.
5. A private company needs to have only two directors.
6. A private company is not required to keep an index of members.
7. There is no restriction on the amount of loans to directors in a private company.

Public Company:
A public company means a company which is not a private company. As perthe Indian Companies Act, a public company is one which:

1. has a minimum paid-up capital of Rs. 5 lakhs
2. has a minimum of 7 members and no limit on maximum members
3. can transfer its shares
4. can invite the public to subscribe to its shares.

A private company which is a subsidiary of a public company is also treated as a public company. A public company’must use the word limited after its name

Difference between a public company and private company:

A Comparative assessment of different forms of business organisation:

Choice of business organisation:
The important factors determining the choice of organization are:
1. Cost and Ease of formation:
From the point of view of cost, sole proprietorship is the preferred form as it involves least expenditure and the legal requirements are minimum. Company form of organisation, is more complex and involves greater costs.

2. Liability:
In case of sole proprietorship and partnership firms, the liability of the owners/ partners is unlimited. In cooperative societies and companies, the liability is limited. Hence, from the point of view of investors, the company form of organisation is more suitable as the risk involved is limited.

3. Continuity:
The continuity of sole proprietorship and partnership firms is affected by death, insolvency or insanity of the owners. However, such factors do not affect the continuity of cooperative societies and companies. In case the business needs a permanent structure, company form is more suitable.

4. Management ability:
If the organisation’s operations are complex in nature and require professionalized management, company form of organisation is a better alternative.

5. Capital:
If the scale of operations is large, company form may be suitable whereas for medium and small sized business one can opt for partnership or sole proprietorship.

6. Degree of control:
If direct control over business and decision making power is required, proprietorship may be preferred. But if the owners do not mind sharing control and decision making, partnership or company form of organisation can be adopted.

7. Nature of business:
If direct personal contact is needed with the customers, Sole proprietorship may be more suitable. Otherwise, the company form of organisation may be adopted.

 

Students can Download Chapter 4 Business Services Notes, Plus One Business Studies Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Business Studies Notes Chapter 4 Business Services

Contents

• Meaning – Nature of Service – Differences between Services and Goods – Types of services
• Banks – Types of banks – Commercial bank – Functions of Commercial bank – e-Banking – Benefits of e-banking
• Insurance – Functions of insurance – Principles of insurance
• Types of insurance – Life insurance – Fire insurance – Marine insurance
• Communication services – Postal services Telecom services
• Transportation – Functions of Transportation
• Warehouse – Functions – Types of warehouses Services are those identifiable, essentially intangible activities that provides satisfaction of wants. For example, consulting a doctor for medical help, getting legal opinion from an advocate etc.

Nature of Services:
1. Intangibility:
Services are intangible, i.e., they cannot be touched. They are experiential in nature, eg: Treatment by a doctor.

2. Inconsistency:
Since there is no tangible product, services have to be performed according to the demand and expectations of the different customers, eg: Mobile services/Beauty parlour.

3. Inseparability:
Another important characteristic of services is the simultaneous activity of production and consumption being performed, i.e. They are inseparable, eg: ATM may replace clerk but presence of customer is a must.

4. Less Inventory:
Services cannot be stored for future use.

5. Involvement:
Participation of the customer in the service delivery is a must.

Difference between Services and Good:

Service	Goods
An activity or process. e.g., watching a movie in a cinema hall	A physical object, e.g., a video cassette of movie
Heterogeneous	Homogenous
Intangible e.g., doctor treatment	Tangible e.g., medicines
Different customers having different Demands, e.g. mobile services	Different customers getting standardised demands fulfilled.
Simultaneous production and consumption, eating an ice-cream in a restaurant	Separation of production and consumption, e.g., purchasing ice cream from a store
Cannot be kept in stock.	Can be kept in stock
participation of customers at the time of service delivery	Involvement at the time of delivery not possible

Types of service:
1. Business Services:
Business services are those services which are used by business enterprises for the conduct of their activities. For example, banking, insurance etc.

2. Social Services: Social services are generally provided voluntarily in pursuit of certain social goals. Eg. improve the standard of living for weaker sections of society, to provide educational services to their children etc.

3. Personal Services: Personal services are those services which are experienced differently by different customers, eg: tourism, restaurants, etc. Banking.

According to Banking Regulation Act 1949, banking means “accepting, for the purpose of lending and investment of deposits of money from the public, repayable on demand or otherwise and withdrawable by cheques, draft, order or otherwise”. Banks can be classified into the following:

1. Commercial banks
2. Cooperative banks
3. Specialised banks
4. Central bank

1. Commercial Banks:
Commercial Banks are banking institutions that accept deposits and grant short-term loans and advances to their customers. There are two types of commercial banks, public sector and private sector banks.
(a) Public Sector Bank:
Public sector banks are those banks, which are owned and managed by the Government. eg. SBI, PNB, IOB etc. Presently there are 28 public sector banks in India

(b) Private Sector Bank:
Private sector banks are owned and managed by private parties. Eg. HDFC Bank, ICICI Bank, Kotak Mahindra Bank and Jammu and Kashmir Bank etc. ICICI bank is the largest private sector bank in India.

2. Cooperative Banks:
Cooperative Banks are governed by the provisions of State Cooperative Societies Act. They managed on the principles of co-operation, self help and mutual help.

3. Specialised Banks:
Specialised banks are foreign exchange banks, industrial banks, development banks, export-import banks which provide financial aid to industries, joint venture projects and foreign trade.

4. Central Bank:
The Central bank supervises, controls and regulates the activities of all the commercial banks of that country. It also acts as a government banker. It controls and coordinates currency and credit policies of any country. The Reserve Bank of India is the central bank of our country.

Insurance:
Insurance is an agreement between two parties whereby one party undertakes, in exchange for a consideration, to pay the other party an agreed sum of money to compensate the loss, damage or injury caused as a result of some unforeseen events.

• Policy: The agreement or contract entered into by the insured and insurer is known as a ‘policy’.
• Insurer: The firm which insures the risk of loss is known as ‘insurer’.
• Insured: The person whose risk is insured is called ‘insured’.
• Premium: The consideration in return for which the insurer agrees to compensate the insured is known as ‘Premium’.

Functions of Insurance:
1. Providing certainty:
Insurance provides certainty of payment for the risk of loss. The insurer charges premium for providing the certainty

2. Protection:
Insurance provides protection from probable chances of loss.

3. Risk sharing:
Insurance helps in sharing of risk. The premium collected from a large number of people are used for compensating the loss of a few.

4. Assist in capital formation:
The accumulated funds of the insurer received by way of premium are invested in various income generating schemes.

Principles of Insurance:

1. Utmost good faith:
The insured must disclose all material facts about the subject matter to the insured. Otherwise the insurer can cancel the contract. The insurer must disclose all the terms and conditions jn the insurance contract to the insured.

2. Insurable interest:
The insured must have an insurable interest in the subject matter of insurance. Insurable interest means the interest shown by the insured in the continued existence of the subject matter or the financial loss he is subjected to on the happening of an event against which it has been insured.

3. Indemnity:
All insurance contracts, except life insurance are contracts of indemnity. According to the principle of indemnity, in the event of occurrence of loss, the insured will be indemnified to the extent of the actual value of his loss or the sum insured which ever is less. The objective behind this principle is nobody should treat insurance contract as the source of profit.

4. Subrogation:
According to this principle, after the insured is compensated for the loss to the property insured by him the right of ownership of such property passes on to the insurer. This is because the insured should not be allowed to make any profit, by selling the damaged property.

5. Causa proxima:
When the loss is the result of two or more causes, the proximate cause for the loss alone will be considered by the insurance company for admitting the claim.

6. Contribution:
In certain cases, the same subject matter is insured with one or more insurer. In case there is a loss, the insured is eligible to receive a claim only up to the amount of actual loss suffered by him.

7. Mitigation of loss:
This principle states that it is the duty of the insured to take reasonable steps to minimize the loss or damage to the insured property. If reasonable care is not taken then the claim from the insurance company may be rejected.

Types of Insurance:

Life Insurance:
It is a contract whereby the insurer undertakes to pay a certain sum of money either on the death of the insured or on the expiry of a specified period of time in consideration of a certain amount (premium) paid by the insured either in lump sum or in installments.
Elements of Life insurance contract:

1. The life insurance contract must have all the essentials of a valid contract
2. Life insurance is a contract of utmost good faith
3. The insured must have insurable interest in the life assured
4. Life insurance is not a contract of indemnity

Types of life insurance policies:
1. Whole Life Policy:
In this kind of policy, the sum assured becomes payable only on the death of the policy holder.

2. Endowment Life Policy:
Here, the sum assured becomes payable either at the end of the stipulated period or on the premature death of the policyholder which ever is earlier.

3. Joint Life Policy:
Under this policy, the lives of two or more persons are insured jointly. The sum assured becomes payable on the death of any one, to the survivor. Usually, this policy is taken up by husband and wife jointly or by two partners of the firm.

4. Annuity Policy:
Under this policy, the assured sum or policy money is payable after the assured attains a certain age in monthly, quarterly, half yearly or annual installments.

5. Children’s Endowment Policy:
This policy is taken by a person for his/ her children to meet the expenses of their education or marriage. The agreement states that a certain sum will be paid by the insurer when the children attain a particular age.

Fire Insurance:
Fire insurance is a contract whereby the insurer, in consideration of premium, undertakes to compensate the insured for the loss or damage suffered due to fire. The premium is payable in single installment.
A claim for loss by fire must satisfy the two following conditions:

• There must be actual loss;
• Fire must be accidental and non intentional.

Elements of Fire insurance contract:

1. The insured must have insurable interest in the subject matter.
2. Fire insurance is a contract of utmost good faith.
3. It is a contract of indemnity.
4. Fire must be the proximate cause of damage or loss.

Marine Insurance:
Marine insurance is an agreement by which the insurance company agrees to indemnify the owner of a ship or cargo against risks which are incidental to marine adventures. eg: collision with other ship, collision of ship with the rocks, fire, storm etc. Marine insurance insures ship hull, cargo and freight.
Elements of Marine insurance contract:

1. Marine insurance is a contract of indemnity
2. It is a contract of utmost good faith
3. Insurable interest must exist at the time of loss
4. The principle of causa proxima will apply to it.

There are three types of Marine insurance. They are:
Ship or hull insurance:
when the owner of a ship is insured against loss on account of perils of the sea, it is known as Ship or Hull insurance.

Cargo insurance:
Marine insurance that covers the risk of loss of cargo is known as Cargo Insurance.

Freight insurance:
The shipping company may seek insurance of the risk of loss of freight. Such a marine insurance is known as freight insurance.

Differences between Life, Fire and Marine insurance:

Communication services:
Communication services are helpful to business for establishing links with the outside world viz., suppliers, customers, competitors etc. The main services which help business can be classified into postal and telecom.
1. Postal services:
Indian post and telegraph department provides various postal services across India. Various facilities provided by postal department are:
(a) Financial facilities:
They provide postal banking facilities to the general public and mobilise their savings through the saving schemes like public provident fund (PPF), Kisan Vikas Patra, National Saving Certificate, Recurring Deposit Scheme and Money Order facility.
(i) Mail facilities: Mail services consist of

• Parcel facilities that is transmission of articles from one place to another
• Registration facility to provide security of the transmitted articles
• Insurance facility to provide insurance cover for all risks in the course of transmission by post.

(b) Allied Postal Services

1. Greetings Post: Greetings card can be sent through post offices.
2. Media Post: Corporate can advertise their brands through post cards, envelops etc.
3. Speed Post: It allows speedy transmission of articles to people in specified cities.
4. e-bill post: The post offices collect payment of telephone, electricity, and water bills from the consumers.
5. Courier Services: Letters, documents, parcels etc. can be sent through the courier service.

2. Telecom Services:
The various types of telecom services are
1. Cellular mobile services:
Mobile communication device including voice and non-voice messages, data services and PCO services utilising any type of network equipment within their service area.

2. Radio paging services:
It means of transmitting information to persons even when they are mobile.

3. Fixed line services:
It includes voice and non-voice messages and data services to establish linkage for long distance traffic.

4. Cable services:
Linkages and switched services within a licensed area of operation to operate media services which are essentially one way entertainment related services.

5. VSAT services (Very small Aperture Terminal):
It is a Satellite based communication service. It offers government and business agencies a highly flexible and reliable communication solution in both urban and rural areas.

6. DTH services (Direct to Home):
It is a Satellite based media services provided by cellular companies with the help of small dish antenna and a set up box.

Transportation:
Transport refers to the activity that facilitates physical movement of goods and individuals from one place to another transportation removes the hindrance of place, i.e., it makes goods available to the consumer from the place of production.
Functions of Transport:

1. Helps in the movement of goods and materials from one place to another
2. Helps in the stabilisation of prices.
3. Helps in the social, economic and cultural development of the country
4. Helps in national and international trade
5. Facilitates large scale production
6. Generates employment opportunities
7. Increases growth of towns and cities
8. Connects all part of the world

Types of Transport:

1. Land Transport
   • Road Transport
   • Rail Transport
   • Pipeline Transport
2. Water Transport
   • Inland water Transport
   • Ocean Transport
3. Air Transport.

Warehousing:
Warehousing means holding or preserving goods in huge quantities from the time of their purchase or production till their consumption. Warehousing is one of the important auxiliaries to trade. It creates time utility by bridging the time gap between production and consumption of goods.
Functions of Warehousing

1. Warehouse helps in supplying the goods to the customers when it is needed.
2. By maintaining a balance of supply of goods warehousing leads to price stabilization.
3. By keeping the goods in the warehouse, the trader can relieve himself of the responsibility of keeping of goods.
4. The warehouse performs the function of dividing the bulkquantity of goods into smaller quantities.
5. Warehousing helps in the seasonal storage of goods to select businesses.
6. The functions of grading, branding and packing of goods can be done in warehouses.
7. The warehousing receipt can be used as a collateral security for obtaining loans.

Types of Warehouses:

(a) Private warehouses: Private warehouses are owned by big business concerns or wholesalers for keeping their own products.

(b) Public warehouses:
They are owned by some agencies, offer storage facilities to the public after charging certain fees. The working of public warehouses is subject to some govt, regulations. They are also known as Duty paid warehouses.

(c) Bonded warehouses:
These warehouses are used to keep the imported goods before the payment of import duties. It offers many advantages to the importer, i.e. The importer can releases the goods in part by paying the proportionate amount of duty. The goods can be branded, blended and packed in the warehouse itself.

(d) Government warehouses:
These warehouses are fully owned and managed by the government. For example, Food Corporation of India, State Trading Corporation, and Central Warehousing Corporation.

(e) Co-operative warehouses:
Marketing co-operative societies and agricultural oo operative societies have set up their own warehouses for members of their cooperative society.

Students can Download Chapter 6 Work, Energy and Power Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 6 Work, Energy and Power

Summary
The Scalar Product

The scalar product (or) dot product of any two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) is defined as

Where ‘q’ is the angle between \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\)
Note: The dot product of A and B is a scalar quantity. Geometrical meaning of \(\overrightarrow{\mathrm{A}}\) . \(\overrightarrow{\mathrm{B}}\)
We know \(\overrightarrow{\mathrm{A}}\) . \(\overrightarrow{\mathrm{B}}\) = ABcosθ
= A(Bcosθ)
= B(A cosθ)

Properties

Question 1.

Answer:

Work Energy Theory
Statement:
The change in kinetic energy of a particle is equal to the work done on it by the net force.
Proof:
We know v² = u² + 2as
v² – u² = 2as
Multiplying both sides with m/2; we get

Work
Definition:
The work done by the force is defined as the product of component of the force in the direction of the displacement and the magnitude of this displacement.
Explanation


Consider a constant force \(\overrightarrow{\mathrm{F}}\) acting on an object of mass m. The object undergoes a displacement d in the positive x direction as shown in the figure. The projection of \(\overrightarrow{\mathrm{F}}\) on d is Fcosθ.
Hence work done w = Fcosθ. d

There are three types of workdone

1. positive workdone
2. negative workdone
3. zero workdone

1. Positive workdone:
Work will be positive, if the displacement has a component in the direction of the force. The angle between force and displacement is zero for positive workdone.
When q = 0 w = Fd
Example

• A person carrying a load climbing up a staircase
• A body being pushed along a surface
• A body falling under gravitation force.

2. Negative workdone:
Work will be negative, if the displacement has a component opposite to the force F. The angle between force and displacement lies between 90° and 180°.
Example

• When a person carrying a load on his head climbs down a staircase, (applied force by him on the load is upwards and the displacement is opposite to it)
• When a body slides along a rough surface the displacement is opposite to the frictional force. Therefore the workdone by the frictional force is negative.

3. Zero work done:
Work will be zero, if there is no component along the direction of force. The angle between applied force and displacement is 90°.
Example
1. When a person carrying a load on his head walks along a level road, the displacement is perpendicular to the force and therefore the work done is zero.

2. In uniform circular motion the centripetal force is along the radius and direction of displacement is along the tangent.

Kinetic Energy
Kinetic energy is the energy possessed by the body because of it’s motion. Kinetic energy of a body of mass m and velocity v,

Workdone By Variable Force

Consider a body moving from x_i to x_f under a variable force. The variation of force with position is shown in graph. Consider a small AB = Dx. The force in this interval is nearly a constant.

Hence workdone to move a body from A to B is. Dw = F(x) Dx.F(x)dx gives the area of rectangle ABCD. When we add successive rectangular areas, we get total work as

When we take Dx tends to zero, the summation can be replaced integration.

Work Energy Theory For A Variable Force
Work energy theorem for a variable force can be derived from work energy theorem of constant force. According work energy theorem for constant force, Change in kE = work done
dk = dw
dk = F dx
Integrating from the initial position (x_i) to (x_f) we get

Concept Of Potential Energy
Potential energy of a body is the energy possessed by it because of its position.
Explanation
Considera mass ‘m’on the surface of the earth. If this mass is raised to height ‘h’ against force of gravity,
work done w = Force × displacement
w = mg × h
w = mgh
This work gets stored as gravitational potential energy.
ie; Gravitational energy V = mgh.

1. Relation between gravitational potential and gravitational force:
If we take negative of the derivative of V(h) with respect to height (h), we get

Where F is gravitational force. The above equation shows that gravitational force is the negative derivative of gravitational potential.

2. Relation between kinetic energy and gravitational potential energy:
Considera body of mass ‘m’ at a height ‘h’ from the surface of the earth. The potential energy at height h
pE = mgh ______(1)
If the body is allowed to fall from this height, it attains kinetic energy,
kE = \(\frac{1}{2}\)mv² _______(2)
But velocity at surface can be found from the formula
v² = u² + 2as
v² = 2gh [Since u = 0, a = g, s = h]
Substituting this value in eq(2), we get
kE = \(\frac{1}{2}\) m2gh
kE = mgh
kE = pE [∵ pE = mgh]

Properties of conservative force:

• A force is conservative, if it can be derived from a scalar quantity (ie F = – \(\frac{d V}{d x}\))
• The workdone by the conservative force depends only on the end points.
• The workdone by conservative force in a closed path is zero.

Conservation of mechanical energy for a freely falling body:

Consider a body of mass ‘m’ at a height h from the ground.
Total energy at the point A
Potential energy at A,
PE = mgh
Kinetic energy, KE = \(\frac{1}{2}\)mv² = 0
(since the body at rest, v = 0).
∴ Total mechanical energy = PE + KE = mgh + 0
= mgh.

Total energy at the point B
The body travels a distance x when it reaches B. The velocity at B, can be found using the formula.
v² = u² + 2as
v² = 0 + 2 gx
∴ KE at B, = \(\frac{1}{2}\)mv²
\(\frac{1}{2}\)m2gx
= mgx
P.E. at B, = mg (h – x)
Total mechanical energy = PE + KE
= mg (h – x) + mgx = mgh.

Total energy at C
Velocity at C can be found using the formula
v² = u² + 2as
v² = 0 + 2gh
∴ KE at C, = \(\frac{1}{2}\)mv²
\(\frac{1}{2}\)m2gh
= mgh
P.E. at C = 0
Total energy = PE + KE
= 0 + mgh = mgh.

The Potential Energy Of A Spring
Hooks law:
The restoring force developed in the spring is proportional to the displacement x and it is opposite to the displacement,
ie Fα – x

Where k is a constant called the spring constant.
Potential energy stored in a spring:

Consider a massless spring fixed to a rigid support at one end and a body attached to the other end. The body moves on a frictionless surface.

If a body is displaced by a distance dx, The work done for this displacement
dw = Fdx
∴ Total work done to move the body from x = 0 to x


This workdone is stored a potential energy in a spring. Hence potential energy of a spring.

Spring force is a conservative force:
If the spring is displaced from an initial position x_i to x_f and again to x_i;

W = 0
This zero workdone means that spring force is conservative.
Energy of a oscillating spring at any point:

If the block of mass ‘m’ (attached to massless spring) is extended to x_m and released, it will oscillate in between +x_m and -x_m. The total mechanical energy at any point x, (lies between -x_m and +x_m) is

This block mass ‘m’ has maximum velocity at equilibrium equi¬librium position (x = 0). At this position, the potential energy stored in a spring is completely converted in to kinetic energy.

Graphical variation of energy

The Law Of Conservation Of Energy
Statement:
Energy cannot be created or destroyed. It can be transformed from one form to another.

Question 2.
Prove conservation of energy for a freely falling body.
Answer:
Conservation of mechanical energy for a freely falling body:

Consider a body of mass ‘m’ at a height h from the ground.
Total energy at the point A
Potential energy at A,
PE = mgh
Kinetic energy, KE = \(\frac{1}{2}\)mv² = 0
(since the body at rest, v = 0).
∴ Total mechanical energy = PE + KE = mgh + 0
= mgh.

Total energy at the point B
The body travels a distance x when it reaches B. The velocity at B, can be found using the formula.
v² = u² + 2as
v² = 0 + 2 gx
∴ KE at B, = \(\frac{1}{2}\)mv²
\(\frac{1}{2}\)m2gx
= mgx
P.E. at B, = mg (h – x)
Total mechanical energy = PE + KE
= mg (h – x) + mgx = mgh.

Total energy at C
Velocity at C can be found using the formula
v² = u² + 2as
v² = 0 + 2gh
∴ KE at C, = \(\frac{1}{2}\)mv²
\(\frac{1}{2}\)m2gh
= mgh
P.E. at C = 0
Total energy = PE + KE
= 0 + mgh = mgh.

Various Form Of Energy
1. Heat:
Heat is a one form of energy, it is the internal energy of molecule.

2. Chemical energy:
Chemical energy arises from the fact that the molecules participating in the chemical reaction have different binding energies.

If the total energy of the reactants is more than the products of the reaction, heat is released and the reaction is said to be exothermic reaction. If the heat is absorbed in chemical reaction it is called endothermic.

3. Electrical energy:
The flow of electrons produce electric current.

4. The equivalence of mass and energy Mass and energy are equivalent and are related by the relation. E = mc², where C, the speed of light in. vacuum.

Question 3.
How much energy will be liberated, when 1 Kg. matter converts in to energy?
Answer:
Energy liberated E = mc²
E = 1 × (3 × 10⁸)²
= 9 × 10¹⁶J.

5. Nuclear energy:
Nuclear energy is obtained from the sun. In this case four light hydrogen nuclei fuse to form a helium nucleus, whose mass is less than the sum of the masses of the reactants. This mass difference (called the mass defect on) is the source of energy.

Power
Power is defined as the time rate at which work is done.

Expression for power in terms of F and V:
The work done (dw) by a force F for a displacement dr is


Where \(\overrightarrow{\mathrm{V}}\) is the instantaneous velocity when the force is \(\overrightarrow{\mathrm{F}}\).
Unit:
Unit of power is watt. 1 watt = 1J/S.
There is another unit of power, namely the horse power (hp)
1 hp = 746w
Kilowatt hour kwh:
Kilowatt hour (kwh) is the unit of energy used to mea-sure electrical energy. One kilowatt hour is the energy consumed in one hour at the rate of 1000 watts/ second.
1 kwh = 1000 watts × 60 × 60 seconds
= 3.6 × 106ws
1 kwh = 3.6 × 106J
Note : kwh is a unit of energy and not of power.

Collisions
There are two types of collisions.

1. Elastic collision
2. Inelastic collision

1. Elastic collision:
Elastic collision is one in which both momentum and kinetic energy are conserved.
Eg:

• collision between molecules and atoms
• collision between subatomic particles.

Characteristics of elastic collision:

• Momentum is conserved
• Total energy is conserved
• K. E. is conserved
• Forces involved during collision are conservative forces

2. Inelastic collision:
Inelastic collision is one in which the momentum is conserved, but KE is not conserved.
Example.

• Mud thrown on a wall
• Any collision between macroscopic bodies in every day life.

Characteristics of inelastic collision:

• Momentum is conserved
• Total energy is conserved
• K.E. is not conserved
• Forces involved are not conservative
• Part or whole of the KE is converted into other forms of energy like heat, sound, light etc.

2. Collisions in one Dimension:
If the initial velocities and final velocities of both the bodies are along the straight line, then it is called one dimensional motion.

Consider two bodies of masses m₁ and m₂ moving with velocities u₁ and u₂ in the same direction and in the same line. If u₁ > u₂ they will collide. After collision let v₁ and v₂ be their velocities.
By conservation of linear momentum.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ ______(1)
m₁u₁ – m₂u₂ = m₁v₁ – m₂v₂ ______(2)
This is an elastic collision, hence K.E. is conserved.

To find v₁ and v₂:


Discussion
Case -1 Mass of two bodies are equal
(i.e. m₁ = m₂ = m). Substitute these values in (7) and (8), we have

ie. bodies exchange their velocities.

Case – 2 (If u₂ =0 and m₂ >> m₁ ie; m₁ – m₂ ≈ -m₂, m₁ + m₂ ≈ -m₂)

The second body remains at rest while the first body rebounds with the same velocity.
Collisions in Two Dimensions:

Consider two bodies of masses m₁ and m₂ moving with velocities u₁ and u₂ along parallel lines. If u₁ > u₂ they will collide. Let v₁ and v₂ be their velocities after collision along directions θ₁ and θ₂. v₁ and v₂ can be resolved in to v₁ cosθ₁, v₂cosθ₂ parallel to x axis and v₁ sinθ₁ and v₂sinθ₂ parallel to y axis.
By conservation of momentum parallel to X-axis,

m₁u₁ + m₂u₂ = m₁v₁ cosθ₁ + m₂v₂ cosθ₂
By conservation of momentum parallel to y-axis.
m₁v₁sinθ₁ + m₂v₂ sinθ₂ = 0 + 0 = 0
By conservation of energy

Students can Download Chapter 10 Functions Notes, Plus One Computer Science Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Computer Science Notes Chapter 10 Functions

Concept of modular programming:
The process of converting big and complex programs into smaller programs is known as modularisation. This small programs are called modules or sub programs or functions. C++ supports modularity in programming called functions
Merits of modular programming:

• It reduces the size of the program
• Less chance of error occurrence
• Reduces programming complexity
• Improves reusability

Demerits of modular programming:
While dividing the program into smaller ones extra care should be taken otherwise the ultimate result will not be right.

Functions in C++:
Some functions that are already available in C++ are called pre-defined or built in functions. In C++, we can create our own functions for a specific job or task, such functions are called user defined functions. A C++ program must contain a main() function. A C++ program may contain many lines of statements(including so many functions) but the execution of the program starts and ends with main() function.

Pre-defined functions:
To invoke a function that requires some data for performing the task, such data is called parameter or argument. Some functions return some value back to the called function.

String functions:
To manipulate string in C++ a header file called string.h must be included.
1. strlen():
to find the number of characters in a string(i.e. string length).
Syntax: strlen(string);
eg:
cout<<strien(“Computer”); It prints 8.

2. strcpy():
It is used to copy second string into first string.
Syntax: strcpy(string1, string2);
eg:
strcpy(str,”BVM HSS”);
cout<<str; It prints BVM HSS.

3. strcat():
It is used to concatenate second string into first one.
Syntax: strcat(string1,string2)
eg:
strcpy(str1,’’Hello”);
strcpy(str2,” World”);
strcat(str1 ,str2);
cout<<str1; It displays the concatenated string “Hello World”

4. strcmp():
It is used to compare two strings and returns an integer.
Syntax: strcmp(string1,string2)

• if it is 0 both strings are equal.
• if it isgreaterthan 0(i.e. +ve) stringl is greater than string2
• if it is less than 0(i.e. -ve) string2 is greater than stringl

eg:
#include<iostream>
#include<cstring>
using namespace std;
int main()
{
char str1 [10],str2[10];
strcpy(str1,”Kiran”);
strcpy(str2,”Jobi”);
cout<<strcmp(str1 ,str2);
}
It returns a +ve integer.

5. strcmpi():
It is same as strcmpO but it is not case sensitive. That means uppercase and lowercase are treated as same.
eg: “ANDREA” and “Andrea” and “andrea” these are same.
#include<iostream>
#include<cstring>
using namespace std;
int main()
{
char str1 [10],str2[10];
strcpy(str1,”Kiran”);
strcpy(str2,”KIRAN”);
cout<<strcmpi(str1 ,str2);
}
It returns 0. That is both are same.

Mathematical functions:
To use mathematical functions a header file called math.h must be included.
1. abs():
To find the absolute value of an integer.
eg: cout<<abs(-25); prints 25.
Cout<<abs(+25); prints 25.

2. sqrt():
To find the square root of a number.
eg: cout<<sqrt(49); prints 7.

3. pow():
To find the power of a number.
Syntax. pow(number1, number2)
eg: cout<<pow(2,10); It is equivalent to 210. It prints 1024.

4. sin():
To find the sine value of an angle and the angle must be in radian. To convert an angle into radian multiply by 3.14(“) and divide by 180.
float x = 60 × 3.14/180;
cout<<sin(x); prints 0.86576.

5. cos():
To find the cosine value of an angle and the angle must be in radian. To convert an angle into radian multiply by 3.14(“) and divide by 180.
float x = 60 × 3.14/180;
cout<<cos(x); prints 0.50046.

Character functions:
To manipulate character in C++ a header file called ctype.h must be included.
1. isupper():
To check whether a character is in uppercase or not. If the character is in uppercase it returns a value 1 otherwise it returns 0.
Syntax: isupper(charch);

2. islower():
To check whether a character is in lowercase or not. If the character is in lowercase it returns a value 1 otherwise it returns 0.
Syntax: islower(char ch);

3. isalpha():
To check whether a character is an alphabet or not. If the character is an alphabet it returns a value 1 otherwise it returns 0.
Syntax: isalpha(char ch);

4. isdigit():
To check whether a character is a digit or not. If the character is a digit it returns a value 1 otherwise it returns 0.
Syntax: isdigit(charch);

5. isalnum():
To check whether a character is an alphanumeric or not. If the character is an alphanumeric it returns a value 1 otherwise it returns 0.
Syntax: isalnum(char ch);

6. toupper():
It is used to convert the given character into uppercase.
Syntax: toupper(char ch);

7. tolower():
It is used to convert the given character into lowercase.
Syntax: tolower(char ch);

Conversion functions:
Some occasions we have to convert a data type into another for this conversion functions used. The header file stdlib.h must be included.
1. itoa():
It is used to convert an integer value to string type.
Syntax: itoa(int v, char str, int size); This function has 3 arguments, first one is the integer to be converted, second is the string variable to store and third is the size of the string.
eg: itoa(“123”,str,4);
cout<<str;

2. atoi():
It Is the opposite of itoa( ). That is it converts a string into integer.
Syntax: atoi(str);

I/O Manipulating function:
It is used to manipulate I /O operations in C++. The header file iomanip.h must be included,
(a) setw(): It is used to set the width for the subsequent string.
Syntax: setw(size);

User defined functions:
Syntax: Return type Function_name(parameterlist)
{
Body of the function
}

• Return type: It is the data type of the value returned by the function to the called function;
• Function name: A name given by the user.

Different types of User defined functions.

• A function with arguments and return type.
• A function with arguments and no return type.
• A function with no arguments and with return type.
• A function with no arguments and no return type.

Prototype of functions:
Consider the following codes
Method 1:
#include<iostream>
using namespace std;
int sum(int n1,int n2)
{
return(n1 + n2);
}
int main()
{
int n1 ,n2;
cout<<“Enter 2 numbers:”;
cin>>n1>>n2;
cout<<“The sum is “<<sum(n1,n2);
}

Method 2:
#include<iostream>
using namespace std;
int main()
{
int n1 ,n2;
cout<<“Enter 2 numbers:”;
cin>>n1>>n2;
cout<<“The sum is “<<sum(n1,n2);
}
int sum(int n1 ,int n2)
{
return(n1 + n2); ‘
}
In method 1 the function is defined before the main function. So there is no error. In method 2 the function is defined after the main function and there is an error called “function sum should have a prototype”.

This is because of the function is defined after the main function. To resolve this a prototype should be declared inside the main function as follows.

Method 3:
#include<iostream>
using namespace std;
int main()
{
int n1,n2;
int sum(int.int);
cout<<“Enter 2 numbers:”;
cin>>n1>>n2;
cout<<“The sum is “<<sum(n1,n2);
}
int sum(int n1,int n2)
{
retum(n1 + n2);
}

Functions with default arguments:
We can give default values as arguments while declaring a function. While calling a function the user doesn’t give a value as arguments the default value will be taken. That is we can call a function with or without giving values to the default arguments.

Methods of calling functions:
Two types call by value and call by reference.
1. Call by value:
In call by value method the copy of the original value is passed to the function, if the function makes any change will not affect the original value.

2. Call by reference:
In call by reference method the address of the original value is passed to the function, if the function makes any change will affect the original value.

Scope and life of variables and functions:
1. Local scope:
A variable declared inside a block can be used only in the block. It cannot be used any other block.
eg:
#include<iostream>
using namespace std;
int sum(int n1,int n2)
{
int s;
s = n1 + n2;
return(s);
}
int main()
{
int n1,n2;
cout<<“Enter 2 numbers:”;
cin>>n1>>n2;
cout<<“The sum is “<<sum(n1,n2);
}
Here the variable s is declared inside the function sum and has local scope;

2. Global scope:
A variable declared outside of all blocks can be used any where in the program.
#include<iostream>
using namespace std;
int s;
int sum(int n1,int n2)
{
s = n1 + n2;
return (s);
}
int main()
{
int n1 ,n2;
cout<<“Enter 2 numbers :”;
cin>>n1>>n2;
cout<<“The sum is “<<sum(n1 ,n2);
}
Here the variable s is declared out side of all functions and we can use variable s any where in the program

Recursive functions:
A function calls itself is called recursive function.

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Kerala Plus One Physics Notes Chapter 2 Units and Measurement

Summary
Introduction

a. Fundamental or base quantities:
Physics is based on measurement of physical quantities. Certain physical quantities are chosen as fundamental or base quantities. Length, mass, time, electric current thermodynamic temperature, amount of substance and luminous intensity are such base quantities.

b. Units: Fundamental Units and Derived Units Unit:
Measurement of any physical quantity is made by comparing it with a standard. Such standard of measurement are known as unit. If length of rod is 5 m, it means that the length of rod is 5 times the standard unit ‘metre’.

Fundamental Unit:
The unit of fundamental or base quantities are called fundamental or base units. The base units are listed in table.

Base quantity	Base unit
Length	Metre
Mass	kilogram
Time	Second
Electric current	Ampere
Thermodynamic Temperature	Kelvin
Amount of Substance	mole
Luminous Intensity	Candela

Derived Unit
The units of other physical quantities can be expressed as combination of base units. Such units are called derived units.
Example: Unit of force is kgms^-2 (or Newton). Unit of velocity is ms^-1.

The International System Of UnitsDerived Unit
System of Units: A complete set of fundamental and derived units is called a system of unit.

a. Different system of units:
The different systems of units are CGS system FPS (or British) system, MKS system and SI system. A comparison of these systems of unit is given in the table below, (for length, mass and time)

Note: The first three systems of units were used in earlier time. Presently we use SI system.

b. International System Of Unit (Si Unit):
The internationally accepted system of unit for measurement is system international d’ unites (French for International System of Units). It is abbreviated as SI.

The SI system is based on seven fundamental units and these units have well defined and internationally accepted symbols, (given in table – 2.1)

c. Solid Angle and Plane Angle:
Other than the seven base units, two more units are defined.
1. Plane angle (dq): It is defined as ratio of length of arc (ds) to the radius, r.


The unit of plane angle is radian. Its symbol is rad.

2. Solid Angle (dW): It is defined as the ratio of the intercepted area (dA) of spherical surface, to square of its radius.


The unit of solid angle is steradian. The symbol is Sr.

Measurement Of Length
Two methods are used to measure length

• direct method
• indirect method.

The metre scale, Vernier caliper, screwgauge, spherometer are used in direct method for measurement of length. The indirect method is used if range of length is beyond the above ranges.

1. Measurement Of Large Distances:
Parallax Method:
Parallax method is used to find distance of planet or star from earth. The distance between two points of observation (observatories) is called base. The angle between two directions of observation at the two points is called parallax angle or parallactic angle (q).

Parallax Method
The planet ‘s’ is at a distance ‘D’ from the surface of earth. To measure D, the planet is observed from two observatories A and B (on earth). The distance between A and B is b and q be the parallax angle between direction of observation from A and B.

AB can be considered as an arch A h B of length ‘b’ of a circle of radius D with its center at S. (Because q is very small, \(\frac{b}{D}\)<<1], Thus from arch-radius relation.

Thus by measuring b and q distance to planet can be determined. The size of planet or angular diameter of planet can be measured using the value of D. If the angle a (angle between two directions of observation of two diametrically opposite points on planet) is measured using a


Where d is diameter of planet.

2. Estimation Of Very Small Distances:
Size Of Molecule
Electron microscope can measure distance of the order of 0.6A0 (wavelength of electron).

3. Range Of Lengths:
The size of the objects in the universe vary over a very wide range. The table (given below) gives the range and order of lengths and sizes of some objects in the universe.

Units for short and large lengths
1 fermi = 1f = 10^-15m
1 Angstrom = 1A° = 10^-10m
1 astronomical unit = 1AU = 1.496 × 10¹¹m
1 light year = 1/y = 9.46 × 10¹⁵m
(Distance that light travels with velocity of 3 × 10⁸ m/s in 1 year)
1 par sec = 3.08 × 10¹⁶m = 3.3 light year
(par sec is the distance at which average radius of earth’s orbit subtends an angle of 1 arc second).

Measurement Of Mass
Mass is basic property of matter. The S.l. unit of mass is kg. While dealing with atoms and molecules, the kilogram •is an inconvenient unit. In this case there is an important standard unit called the unified atomic mass unit( u).
1 unified atomic mass unit = lu
= (1/12)^th of the mass of carbon-12

1. Range Of Masses:
The masses of the objects in the universe vary over a very wide range which is given in the table.

Measurement Of Time
To measure any time interval we need a clock. We now use an atomic standard of time, which is based on the periodic vibrations produced in a cesium atom. This is the basis of the cesium clock sometimes called atomic clock.

Definition of second:
One second was defined as the duration of 9, 192, 631, 770 internal oscillations between two hyperfine levels of Cesium-133 atom in the ground state.
Range and Order of time intervals

Accuracy, Precision Of Instruments And Errors In Measurement
Error:
The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is called error.

Systematic errors:
The systematic errors are those errors that tend to be in one direction, either positive or negative.

Sources of systematic errors

1. Instrumental errors
2. Imperfection in experimental technique or procedure
3. personal errors

1. Instrumental errors:
Instrumental error arise from the errors due to imperfect design or calibration of the measuring instrument.
eg: In Vernier Callipers, the zero mark of vernier scale may not coincide with the zero mark of the main scale.

2. Imperfection in experimental technique or procedure:
To determine the temperature of a human body, a thermometer placed under the armpit will always give a temperature lower than the actual value of the body temperature. Other external conditions (such as changes in temperature, humidity, velocity……..etc) during the experiment may affect the measurement.

3. Personal Errors:
Personal error arise due to an individual’s bias, lack of proper setting of the apparatus or individual carelessness etc.

Random errors
The random errors are those errors, which occur irregularly and hence are random with respect to sign and size. These can arise due to random and unpredictable fluctuations in experimental conditions (eg. unpredictable fluctuations in temperature, voltage supply, etc.)

Least Count Error
The smallest value that can be measured by the measuring instrument is called its least count. The least count error is the error associated with the resolution of the instrument. By using instruments of higher precision, improving experimental technique etc, we can reduce least count error.

1. Absolute Error, Relative Error And Percentage Error:
The magnitude of the difference between the true value of the quantity and the measured value is called absolute error in the measurement. Since the true value of the quantity is not known, the arithmetic mean of the measured values may be taken as the true value.

Explanation:
Suppose the values obtained in several measurements are a₁, a₂, a₃,………,a_n. Then arithmetic mean can be written as

The absolute error,
∆a₁ = a_mean – a₁
∆a₂ = a_mean – a₂
∆a_n = a_mean – a_n

a. Mean absolute error:
The arithmetic mean of all the absolute errors is known as mean absolute error. The mean absolute error in the above case,

b. Relative error:
The relative error is the ratio of the mean absolute error (Da_mean) to the mean value (a_mean).

c. Percentage error:
The relative error expressed in percent is called the percentage error (da).

Example:
Question 1.
When the diameter of a wire is measured using a screw gauge, the successive readings are found to be 1.11 mm, 1.14mm, 1.09mm, 1.15mm and 1.16mm. Calculate the absolute error and relative error in the measurement.
Answer:
The arithmetic mean value of the measurement is

The absolute errors in the measurements are
1.13 – 1.14 = 0.02mm
1.13 – 1.14 = -0.01mm
1.13 – 1.09 = 0.04mm
1.13 – 1.15 =-0.02 mm
1.13 – 1.16 = 0.03mm
The arithmetic mean of the absolute errors

Percentage of relative error

2. Combination Of Errors:
When a quantity is determined by combining several measurements, the errors in the different measurements will combine in some way or other.

a. Error of a sum or a difference:
Rule: when two quantities are added or subtracted, the absolute error in the final result is the sum of the absolute errors in the individual quantities.
Explanation:
Let two quantities A and B have measured values A ± DA and B ± DB respectively. DA and DB are the absolute errors in their measurements. To find the error Dz that may occur in the sum z = A + B,
Consider
z + ∆z = (A ± ∆A) + B ± ∆B = (A + B) ± ∆A ± ∆B
The maximum possible error in the value of z is given by,

Similarly, it can be shown that, the maximum error in the difference.
Z = A – B is also given by

b. Error of product ora quotient:
Rule: When two quantities are multiplied or divided, the relative error in the result is the sum of the relative errors in the multipliers.
Explanation:
Suppose Z=AB and the measured values of A and B are A + DA and B + DB. They
Z + DZ = (A + DA) (B + DB)
= AB ± BDA ± ADB ± DADB
Dividing LHS by Z and RHS by AB, we get

c. Errors in case of a measured quantity raised to a power:
Suppose Z = A²

Hence, the relative error in A² is two time the error in A.
In general, if \(Z=\frac{A^{P} B^{q}}{C^{T}}\)
Then

Hence the rule: The relative error in a physical quantity raised to the power K is the K times the relative error in the individual quantity.

Significant Figures
Every measurement involves errors. Hence the result of measurement should be reported in a way that indicates the precision of measurement.

Normally, the reported result of measurement is a number that includes all digits in the number that are known reliable plus the first digit that is uncertain. The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
Example:

• The length of a rod measured is 3.52cm. Here there are 3 significant figures. The digits 3 and 5 are reliable and the last digit 2 is uncertain.
• The mass of a body measured as 3.407g. Here there are four significant figures. The figure 7 is uncertain.

When the measurement becomes more accurate, the number of significant figure is increased.
Rules to find significant figures:
1. All the non zero digits are significant.
Example:
Question 1.
Find significant figure of

• 2500
• 263.25

Answer:

• In this case, there are two nonzero numbers. Hence significant figure is 2.
• In this, there are 5 nonzero numbers. Hence significant figure is 5.

2. All the zeros between two nonzero digits are significant, no matter where the decimal point is,
Example:
Question 2.
Find the significant figure

• 2.05
• 302.005
• 2000145

Answer:

• Significant figure is 3
• Significant figure is 6
• Significant figure is 7

3. If the number is less than 1, the zeros on the right of decimal point but to the left to the first nonzero digits are not significant.
Example:
Question 1.
Find the significant figure of

• 0.002308
• 0.000135

Answer:

• 4 significant figures
• 3 significant figures

4. The terminal zeros in a number without a deci¬mal point are not significant.
Example:
Question 1.
Find the significant figure of

• 12300
• 60700

Answer:

• 3
• 3

Note: But if the number obtained is on the basis of actual measurement, all zeros to the right of last non zero digit are significant.
Example: If distance is measured by a scale as 2010m. This contain 4 significant figures.

5. The terminal zeros in a number with a decimal point are significant.
Example:
Question 1.
Find the significant figure of

• 3.500
• 0.06900
• 4.7000

Answer:

• 4
• 4
• 5

Method to find significant figures through scientific notation:
In this notation, every number is expressed as a × 10^b, where a is a number between 1 and 10 and b is any positive or negative power. In this method, we write the decimal after the first digit.
Example:
4700m =4.700 × 10³m
The power of 10 is irrelevant to the determination of significant figures. But all zeros appearing in the base number in the scientific notation are significant. Hence each number in this case has 4 significant figures.
Significant figures in numbers:-

Numbers	Significant figures
1374	4
13.74	4
0.1374	4
0.01374	4
013740	5
1374.0	5
5100	2
51.00	4
5.100	4
3.51 × 103	3
2.1 × 10-2	2
0.4 × 10-4	1

a. Rules for Arithmetic operations with significant figures:
1. Rules for multiplication or division:
In multiplication or division, the computed result should not contain greater number of significant digits than in the observation which has the fewest significant digits.
Examples:
(i) 53 × 2.021 =107.113
The answer is 1.1 × 10² since the number 53 has only 2 significant digits.

(ii) 3700 10.5 = 352.38
The answer is 3.5 × 10² since the minimum number of significant figure is 2 (in the number 3700)

2. Rules for Addition and Subtraction:
In addition or substraction of given numbers, the same number of decimal places is retained in the result as are present in the number with minimum number of decimal places.
Examples:
(i) 76.436 +
12.5
88.936
The answer is 88.9, since only one decimal place is found in the number 12.5.

(ii) 43.6495 +
4.31
47.9595
The answer is 47.96 since only two decimal places are to be retained.

(iii) 8.624 –
3.1726
5.4514
The answer is 5.451

(iv) 6.5 × 10^-5 – 2.3 × 10^-6 = 6.5 × 10^-5 – 0.23 × 10^-5
= 6.27 × 10^-5
The answer is = 6.3 × 10^-5

Dimensions And Dimensional Analysis
All physical quantities can be expressed in terms of seven fundamental quantities. (Mass, length, time, temperature, electric current, luminous intensity and amount of substance). These seven quantities are called the seven dimensions of the physical world.

The dimensions of the three mechanical quantities mass, length and time are denoted by M, L and T. Other dimensions are denoted by K (for temperature), I (for electric current), cd (for luminous intensity) and mol (for the amount of substance).

The letters [L], [M], [T] etc. specify only the nature of the unit and not its magnitude. Since area may be regarded as the product of two lengths, the dimensions of area are represented as [L] × [L] = [L]².

Similarly, volume being the product of three lengths, its dimensions are represented by [L]³. Density being mass per unit volume, its dimensions are M/L³ or M¹L³.

Thus, the dimensions of a physical quantity are the powers to which the fundamental units of length, mass, time must be raised to represent it.
Note: The dimensions of a physical quantity and the dimensions of its unit are the same.

Dimensional Formula And Dimensional Equations
An equation obtained by equating a quantity with its dimensional formula is called dimensional equations of the physical quantities.
Examples:
Consider for example, the dimensions of the following physical quantities.
1. Velocity: Velocity = distance/ time = L/T = L¹T^-1 \The dimension of velocity are, zero in mass, 1 in length and-1 in time.

2. Acceleration:
Acceleration = \(\frac{\text { Change in velocity }}{\text { time }}=\frac{L^{1} T^{-1}}{T}=L^{1} T^{-2}\)

3. Force: Force = mass × acceleration
Dimensions of force = M × L¹T^-2 = M¹L¹T ^-2
That is, the dimensions of force are 1 in mass, 1 in length and -2 in time.

4. Momentum: Momentum = mass × velocity
Dimensions of momentum = M × L¹T^-1 = M¹L¹T ^-1

5. Moment of a force: Moment = force × distance
Dimensions of moment = M¹L¹T^-2 × L = M¹L²T ^-2

6. Impulse: Impulse = force × time
Dimensions of impulse = M¹L¹T^-2 × T = M¹L¹T ^-1

7. Work: Work = force × distance
Dimensions of work = M¹L¹T^-2 × L = M¹L²T ^-2

8. Energy: Energy = Work done
Dimensions of energy = dimensions of work = M¹L²T^-2.

9. Power: Power = work/time
Dimensions of power \(=\frac{M^{2} L^{2} T^{-2}}{T}p\) = M¹L²T^-3

Dimensional Analysis And Its Applications
The important uses of dimensional equations are:

1. To check the correctness of an equation.
2. To derive a correct relationship between different physical quantities.
3. To convert one system of units into another.

1. Checking the correctness of an equation:
For the correctness of an equation, the dimensions on either side must be the same. This ‘ is known as the principle of homogeneity of dimensions.

If an equation contains more than two terms, the dimensions of each term must be the same. Thus, if x = y + z, Dimensions of x = dimensions of y = dimensions of z
Example :
Question 1.
Check the correctness of the equation s = ut + 1/2at² by the method of dimensions.
Dimensions of, s = L¹
Dimensions of, u = L¹T^-1
Dimensions of, ut = L¹T^-1 × T¹ = L¹
Dimensions of, a = L¹T^-2
Dimensions of, at² = L¹T^-2 × T² = L¹
The constant 1/2 has no dimensions. Each term has dimension L¹.
Therefore, dimensions of, ut + 1/2 at² = ¹
Thus, either side of the equation has the same dimen¬sion L1 and hence the equation is dimensionally correct.
Note: Even though the equation is dimensionally correct, it does not mean that the equation is necessarily correct. For instance the equation s = ut + at² is also dimensionally correct, though the correct equation, s = ut + 1/2 at².

2. Deriving the correct relationship between different physical quantities:
The principle of homogeneity of dimensions also helps to derive a relationship between the different physical quantities involved. This method is known as dimensional analysis.
Example :
Question 1.
Deduce an expression for the period of oscillation of a simple pendulum.
The period of the simple pendulum may possibly depend upon

• The mass of the bob, m
• The length of the pendulum, I
• Acceleration due to gravity, g
• The angle of swing, q

Let us write the equation for the time period as t = km^a l^b g^c θ^d
where, k is a constant having no dimensions; a, b, c are to be found out. ’
The dimensions of, t = T¹
Dimensions of m = M¹
Dimensions of, l = L¹
Dimensions of, g = L¹T^-2
Angle q has no dimensions (since, q = arc/radius = L/L) Equating the dimensions of both sides of the equation, we get,
T¹ = M^aL^b (L¹T^-2)^c
ie. T¹ = M^aL^b+cT^-2c
The dimensions of the terms on both sides must be the same. Equating the powers of M, L and T.
a = 0; b + c = 0; -2c = 1
∴ c = \(\frac{-1}{2}\), b = ^–c = \(\frac{1}{2}{/latex]
Hence, the equation becomes,
t = kl^1/2, 2g^-1/2
ie, t = k[latex]\sqrt{l/g}\)
Experimentally, the value of k is found to be 2p.
Limitations of Dimensional Analysis:
The method of dimensional analysis has the following limitations:

• It gives no information about the dimensionless constant involved in the equation.
• The method is not applicable to equations involving trigonometric and exponential functions.
• This method cannot be employed to derive the exact form of the relationship, if it contains sum
  of two, or more terms.
• If the given physical quantity depends on more than three unknown quantities, the method fails.

3. Conversion of one system of units to another:
Suppose we have a physical quantity of dimensions a, b and c in mass, length and time. The dimensional formula for the quantity is therefore, M^aL^bT^c. Let its numerical value be n, in one system in which the fundamental units of mass, length and time are M₁, L₁ and T₁ respectively. Then, the magnitude of the physical quantity
= n₁ M₁^aL₁^bT₁^c
Also, let the numerical value of the same quantity be n₂ in another system where the fundamental units of mass, length and time are M₂, L₂ and T₂respectively. Then the magnitude of the quantity
= n₂ M₂^aL₂^bT₂^c
Equating, n₂ M₂^aL₂^bT₂^c =
n₁ M₁^aL₁^bT₁^c

Example :
Question 1.
Find the number of dynes in one newton.
Answer:
Dyne is the unit of force in the C.G.S. system and newton is the S.I.unit. The dimensional formula for force is M¹L¹T^-2. In eqn. (1) let the suffix 1 refer to quantities in S.I and 2 those in the C.G.S. system.
Here, a = 1, b = 1 and c = 2

and n₁ = 1 (ie. one Newton)
By eqn. (1),
n₂ = 1 (1000)¹ (100)¹ (1)^-2 = 10⁵
ie. 1 newton = 10⁵ dynes.

Students can Download Chapter 9 String Handling and I/O Functions Notes, Plus One Computer Science Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Computer Science Notes Chapter 9 String Handling and I/O Functions

Summary
String handling using arrays:
A string is a combination of characters hence char data type is used to store string. A string should be enclosed in double quotes. In C++ a variable is to be declared before it is used.Eg. “BVM HSS KALPARAMBU”.

Memory allocation for strings:
To store “BVM” an array of char type is used. We have to specify the size. Remember each and every string is end with a null (\0) character. So we can store only size- 1 characters in a variable. Please note that \0 is treated as a single character. \0 is also called as the delimiter.
char school_name[4]; By this we can store a maximum of three characters.

Consider the following declarations

• char my_name[10] = ”Andrea”;
• char my_name2[ ] = ”Andrea”;
• char str[ ] = ”Hello World”

In the first declaration 10 Bytes will be allocated but it will use only 6 + 1 (one for ‘\0’) = 7 Bytes the remaining 3 Bytes will be unused. But in the second declaration the size of the array is not mentioned so only 7 Bytes will be allocated and used hence no wastage of memory.

Similarly in the third declaration the size of the array is also not mentioned so only 12( one Byte for space and one Byte for ‘\0’) Bytes will be allocated and used hence no wastage of memory

Input/output operations on strings:
Consider the following code
#include<iostream>
using namespace std;
int main()
{
char name[20];
cout<<“Enter your name:”;
cin>>name;
cout<<“Hello “<<name;
}
If you run the program you will get the prompt as follows
Enter your name: Alvis Emerin
The output will be displayed as follows and the “Emerin” will be truncated.
Hello Alvis
This is because of cin statement that will take upto the space. Here space is the delimiter. To resolve this gets() function can be used. To use gets() and puts() function the header file stdio.h must be included. gets() function is used to get a string from the keyboard including spaces.

puts() function is used to print a string on the screen. Consider the following code snippet that will take the input including the space.
#include<iostream>
#include<cstdio>
using namespace std;
int main()
{
char name[20];
cout<<“Enter your name:”;
gets(name);
cout<<“Hello “<<name;
}

More console functions:

Stream functions for I / O operations:
Somefunctions that are available in the header file iostream.h to perforrn I/O operations on character and strings(stream of characters). It transfers streams of bytes between memory and objects. Keyboard and monitor are considered as the objects in C++.

Input functions:
The input functions like get( )(to read a character from the keyboard) and getline() (to read a line of characters from the keyboard) is used with cin and dot(.) operator.

eg:
#include<iostream>
using namespace std;
int main()
{
char str[80],ch=’z’;
cout<<“enter a string that end with z:”;
cin.getline(str,80,ch);
cout<<str;
}
If you run the program you will get the prompt as follows
Enter a string that end with z: Hi I am Jobi. I am a teacher. My school is BVM HSS The output will be displayed as follows and the string after ‘z’ will be truncated.
Hi, I am Jobi. I am a teacher

Output function:
The outputt functions like put() (to print a character on the screen) and write() (to print a line of characters on the screen) is used with cout and dot(.) operator.

 

Students can Download Chapter 4 Motion in a Plane Notes, Plus One Physics Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Notes Chapter 4 Motion in a Plane

Summary
Introduction
In this chapter, we will study, about vector, its ’ addition, substraction and multiplication We then discuss motion of an object in a plane. We shall also discuss uniform circular motion in detail.

Scalars And Vectors

a. Scalars:
A quantity which has only magnitude and no direction is called a scalar quantity.
Eg: length; volume, mass, time, work etc.

b. Vectors:
(i) The need for vectors:
In one dimensional motion, there are only two possible directions. But in two or three dimensional motion, infinite number of directions are possible. Hence quantities like displacement, velocity, force etc. cannot be represented by magnitude alone: Therefore in order to describe such quantities, not only magnitude but direction also is essential.

(ii) Vector:
A physical quantity which has both magnitude and direction is called a vector quantity.
Eg: Displacement, Velocity, Acceleration, Force, momentum.

1. Position and Displacement Vectors:
Position vector:
Consider the motion of an object in a plane. Let P be the position of object at time tw.r.t.origin given O.

A vector representing the position of an object P with respect to an origin O is called position vector \(\overrightarrow{\mathrm{OP}}\) of the object. This position vector may be represented
by an arrow with tail at O and head at P.

The length of the line gives the magnitude of the vector and arrow head (tip) indicates its direction in space. The magnitude of OP is represented by |\(\overrightarrow{\mathrm{OP}}\)|.

Displacement vector:

Consider the motion of an object in a plane. Let P be the position of a moving object at a time t and p¹ that at a later time t¹. \(\overrightarrow{\mathrm{OP}}\) and \(\overrightarrow{\mathrm{OP}^{1}}\) are the position vectors at time t and t¹ respectively. So the vector \(\overrightarrow{\mathrm{PP}^{1}}\) is called displacement vector corresponding to the motion in the time interval (t – t¹).

2. Equality of vectors:
Two vectors are said to be equal if they have the same magnitude and direction.

The above figure shows two vectors \(\vec{A}\) and \(\vec{B}\) having the same magnitude and direction.
∴ \(\vec{A}\) = \(\vec{B}\).

Question 1.
Observe the following figures (a) and (b) and find which pair does represents equal vectors?

Answer:
Figure a represent that A and B are equal vectors. Two vectors A¹ and B¹ are unequal, because they were in different directions.

Multiplication Of Vectors By Real Numbers
Multiplying a vector \(\vec{A}\) with a positive number I gives a vector whose magnitude is changed by the factor λ.

The direction λ\(\vec{A}\) is the same as that of \(\vec{A}\).
Examples:

A vector \(\vec{A}\) and the resultant vector after multiplying \(\vec{A}\) by a positive number 2.

A vector A and resultant vector after multiplying it by a negative number-1 and -1.5.

Addition And Subtraction Of Vectors – Graphical Method
Vectors representing physical quantities of the same dimensions can be added or subtracted. The sum of two or more vectors is known as their resultant.

1. When two vectors are acting in the same direction:

2. When two vectors act in opposite direction:
In this case, the angle between the vectors is 180°.

The resultant of the two vectors is a new vector whose magnitude is the difference between the magnitudes of the two vectors and whose direction is the same as the direction of the bigger vector.

3. When two vectors are inclined to each other:
The sum of two vectors inclined at an angle q can be obtained either by

• the law of triangle of vectors
• the parallelogram law of vectors

(i) Triangle method:
This law states that if two vectors can be represented in magnitude and direction by the two sides of a triangle taken in the same order, then the resultant is represented in magnitude and direction by the third side of the triangle taken in the reverse order.

Explanation
Consider two vectors \(\vec{A}\) and \(\vec{B}\) as shown in figure.

(ii) Parallelogram law of vector addition:
This law states that if two vectors acting at a point can be represented in magnitude and direction by the two adjacent sides of a parallelogram, then the diagonal of the parallelogram through that point represents the resultant vector.
Explanation
Consider two vectors \(\vec{A}\) and \(\vec{B}\) as shown in figure.

To find \(\vec{A}\) + \(\vec{B}\), we bring theirtails to a common origin Q as shown below.


The diagonal of parallelogram OQSP, gives the resultantof (\(\vec{R}\) = \(\vec{A}\) + \(\vec{B}\)) of two vectors \(\vec{A}\) and \(\vec{B}\).
Note: Triangle and parallelogram law of vector addition gives the same result, ie. the two methods are equivalent.

4. Substraction of vectors:

To substract \(\vec{B}\) from \(\vec{A}\), reverse the direction of \(\vec{B}\).

Then add –\(\vec{B}\) with \(\vec{A}\) using parallelogram law or tri¬angle law.

The resultant of \(\vec{A}\) and \(\vec{B}\) is given by \(\vec{R}\).
Null vector or zero vector:
A vector having zero magnitude is called a zero vector or null vector. Null vector is represented by \(\vec{O}\). Since the magnitude is zero, we don’t have to specify its direction.
Properties of null vector:

Question 2.
Explain a zero vector using an example.
Answer:
Suppose that an object which is at P at time t, moves to p¹ and then comes back to P. In this case displacement is a null vector.

Resolution Of Vectors Unit Vectors
A vector divided by its magnitude is called unit vector along the direction of that vector. A unit vector in the direction of \(\vec{A}\) is written as \(\hat{A}\).

Orthogonal unit vectors:

In the Cartesian coordinate system, the unit vectors along the X, Y and Z directions are represented by \(\hat{i}\), \(\hat{j}\) and \(\hat{k}\) respectively and are known as orthogonal unit vectors.
For unit vectors

Resolution of vector into rectangular components:
The components of a vector in two mutually perpendicular directions are called its rectangular components.
Explanation

Consider a vector \(\overrightarrow{\mathrm{A}}\) that lies in x-y plane as shown in figure. To resolve \(\overrightarrow{\mathrm{A}}\), draw lines from the head of \(\overrightarrow{\mathrm{A}}\) perpendicularto the coordinate axes as shown below.

The quantities A_x and A_y are called x and y components of the vector \(\overrightarrow{\mathrm{A}}\). Hence the vector \(\overrightarrow{\mathrm{A}}\) can be written in terms of rectangular components as

Magnitude of \(\overrightarrow{\mathrm{A}}\):

From the figure, the magnitude of \(\overrightarrow{\mathrm{A}}\) can be written as,

Question 3.
A vector \(\overrightarrow{\mathrm{A}}\) in xyz plane is given below. A_x, A_y and A_z are the perpendicular components in x,y and z directions respectively.

1. Write \(\overrightarrow{\mathrm{A}}\) in terms of rectangular components.
2. Write the magnitude of \(\overrightarrow{\mathrm{A}}\).

Answer:

The magnitude of vector \(\overrightarrow{\mathrm{A}}\) is

Vector Addition – Analytical Method
The graphical method of adding vectors helps us in visualizing the vectors and the resultant vector. But this method has limited accuracy and sometimes tedious. Hence we use analytical method to add vectors.
Explanation

The vectors obey commutative and associative laws. Hence

Question 4.
Find the magnitude and direction of the resultant of two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{A}}\) in terms of their magnitudes and angle between them.
Answer:

Consider two vectors \(\vec{A}(=\overrightarrow{O P}) \text { and } \vec{B}(=\overrightarrow{O Q})\) making an angle q. Using the parallelogram method of
vectors, the resultant vector \(\overrightarrow{\mathrm{R}}\) can be written as,

SN is normal to OP and PM is normal to OS. From the geometry of the figure
OS² = ON² + SN²
but ON = OP + PN
ie. OS² = (OP+PN)² + SN² ______(1)
From the triangle SPN, we get
PN = Bcosq and SN = Bsinq
Substituting these values in eq.(1), we get
OS² = (OP + Bcosq)² + (Bsinq)²
But OS = R and OP = A
R² = (A + Bcosq)² + B²sin²q
= A² + 2ABcosq + B²cos²q + B²sin²q
R² = A² + 2 ABcosq + B²

The resultant vector \(\overrightarrow{\mathrm{R}}\) make an angle a with \overrightarrow{\mathrm{A}}. From the right angled triangle OSN,

But SN = Bsinq PN = Bcosq

Motion In A Plane

1. Position vector and displacement vector Position vector:

Consider a small body located at P with reference to the origin O. The position vector of the point ‘P’

Displacement vector


where Dx = x¹ – x¹, Dy = y¹ – y
Velocity:
If Dt is the time taken to reach from P to P¹
The average velocity, \(\overrightarrow{\mathrm{v}}_{\mathrm{av}}=\frac{\overrightarrow{\Delta r}}{\Delta \mathrm{t}}\) ____(3)
Substitute eq.(2) in eq.(3), we get

The direction of average velocity is the same as that of \(\overrightarrow{\Delta r}\).
The instantaneous velocity can be written as

Acceleration:
If the velocity of an object changes from \(\overrightarrow{\mathrm{v}} \text { to } \overrightarrow{\mathrm{v}^{1}}\) in time Dt, then its average acceleration is given by

Instantaneous acceleration:
The acceleration at any instant is called instantaneous acceleration. When Dt goes to zero, the average acceleration becomes instantaneous acceleration.
ie. Instantaneous acceleration

Motion In A Plane With Constant Acceleration
Consider an object moving in xy plane with constant acceleration ‘a’. Let \(\vec{u}\) be the initial velocity at t=0 and \(\vec{v}\) be the final velocity at time t.
Then by definition acceleration

In terms of components
v_x = u_x + a_xt
v_y = u_y + a_yt
Displacement in a plane
If \(\overrightarrow{\mathrm{r}_{0}}\) and \(\vec{r}\) be position vectors of particle at t = 0 and time t respectively, then
displacement = \(\vec{r}-\vec{r}_{0}\) _______(1)
For uniformly accelerated motion, displacement,

In terms of components
x = x₀ + u_xt + 1/2 a_xt²
y = y₀ + u_yt + 1/2 a_yt²
The eq.(2) shows that, the above motion in xy plane can be treated as two separate one dimensional motions along two perpendicular directions.

Relative Velocity In Two Dimensions
Consider two bodies A and B moving along a plane with velocities \(\overrightarrow{\mathrm{V}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{V}}_{\mathrm{B}}\). Then velocity of A relative to that of B is,

Similarly velocity of B relative to that of A

Projectile Motion
Projectile:
A body is projected into air and is allowed to move under the influence of gravity is called projectile.

Consider a body which is projected into air with a velocity u at an angle q. The initial velocity ‘u’ can be divided into two components ucosq along horizontal direction and using along vertical direction.

1. Time of flight:
The time taken by the projectile to cover the horizontal range is called the time of flight. Time of flight of projectile is decided by usinq. The time of flight can be found using the formula
s = ut + 1/2 at²
Taking vertical displacement s = 0, a = -g and initial vertical velocity = usinq, we get
0 = usinqt – 1/2gt²
1/2 gt² = usinqt

2. Vertical height:
Vertical height of body is decided by vertical component of velocity (usinq). The vertical displacement of projectile can be found using the formula v² = u² + 2as
When we substitute v=0, a = -g, s = H and u = usinq, we get
0 = (usinq)² + 2 – g × H
2gH = u²sin²q

3. Horizontal Range:
If we neglect the air resistance, the horizontal velocity (ucosq) of projectile will be a constant.
Hence the horizontal distance (R) can be found as
R = horizontal velocity × time of flight

The eq.(3) shows that, R is maximum when sin2q is maximum, ie. When q₀ = 45°.
The maximum horizontal range

Equation for path of projectile

Question 5.
What is the shape of path followed by the projectile? Show that the path of projectile is parabola. The vertical displacement of projectile at any time t, can be found using the formula.
Answer:
S = ut+ 1/2at²
y = usinqt – 1/2gt²
But we know horizontal displacement, x = ucosq × t

In this equation g, q and u are constants. Hence eq.(4) can be written in the form
y = ax + bx²
where a and b are constants. This is the equation of parabola, ie. the path of the projectile is a parabola.

Uniform Circular Motion
The motion of an object along the circumference of a circle is called circular motion.
Uniform circular motion:
When an object follows a circular path at a constant speed, the motion is called uniform circular motion.
Period:
The time taken by the object to complete one full revolution is called the period.
Frequency:
The number of revolutions completed per second is called the frequency u of the circular motion.
If the period of a circular motion isT, its frequency

Angular Displacement (Dq):
The angle Dq in radians swept out by the radius vector in a given interval of time is called the angular displacement of the object.
Angular velocity:
The rate of change of angular displacement is called the angular velocity.

If T is the period of an object, then its radius vector sweeps out an angle of 2p radian.
Therefore in one second it sweeps out an angle \(\frac{2 \pi}{T}\).
∴ Angular velocity of the object

Expression for velocity and acceleration in uniform circular motion:

The direction of velocity is in the direction of tangent at that point. The change in velocity vectors \((\overrightarrow{\Delta v})\) is obtained by triangle law of vector as shown in figure (b).

a. Speed and angular speed in uniform circular motion:
Let the Dq be the angle constructed by the body during the time interval ∆t. The angular velocity can be written as

If the distance travelled by the object during the time Dt is Dr (ie. PP¹ = Ds) then speed

But Ds = RDq
where R = \(|\vec{r}|=|\overrightarrow{r^{\prime}}|\)
Substituting Dr = RDq in eq.(1)
we get

b. Acceleration in uniform circular motion:

The direction of this acceleration should be in the direction of \(\overrightarrow{\Delta V}\). The fig(b) shows that \(\overrightarrow{\Delta V}\) is towards the centre of the circular path. Hence the acceleration is directed towards the centre of the circle and is called centripetal acceleration.

The force which produces this centripetal acceleration is called centripetal force.
Centripetal force can be written as
F = ma_c

But ω = \(\frac{V}{R}\). Hence we get K

Students can Download Chapter 4 Motion in a Plane Questions and Answers, Plus One Physics Chapter Wise Questions and Answers helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Physics Chapter Wise Questions and Answers Chapter 4 Motion in a Plane

Plus One Physics Motion in a Plane One Mark Questions and Answers

Question 1.
A cricketer can throw a ball to a maximum horizontal distance of 100m. With the same speed how much high above the ground can the cricketer throw the same ball?
(a) 200m
(b) 150m
(c) 100m
(d) 50m
Answer:
(d) 50m
R_max = \(\frac{u^{2}}{g}\)
100 = \(\frac{u^{2}}{g}\) or u² = 100g
Using, v² = u² + 2as
0 = (100g) + 2(-g)h or h = 50m.

Question 2.
If vectors \(\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) and \(\hat{\mathrm{i}}-3 \hat{\mathrm{j}}-\mathrm{ak}\) are equal vectors, then the value of a is
(a) 5
(b) 2
(c) -3
(d) -5
Answer:
(d) Comparing vector, we get = \(+5 \hat{k}=-a \hat{k}\)
a = -5.

Question 3.
State which of the following algebraic operations are not meaningful
(a) Addition of a scalar to a vector
(b) Multiplication of any two scalars.
(c) Multiplication of vector by scalar
(d) Division of a vector by scalar Addition of a scalar to a vector
Answer:
(a) Addition of a scalar to a vector

Question 4.
What is the acceleration of train travelling at 40ms^-1 as it goes round a curve of 160m radius?
Answer:
a = \(\frac{v^{2}}{r}=\frac{40 \times 40}{160}\) = ms^-2.

Question 5.
What provides centripetal force in the following cases.

1. Electron revolving around nucleus.
2. Earth revolving around sun

Answer:

1. Electrostatic force
2. Gravitational force

Question 6.
Why a cyclist has to bend inwards while going on a circular track?
Answer:
The cyclist bends inwards to provide required centripetal force.

Question 7.
A body executing uniform circular motion has constant
(i) velocity
(ii) acceleration
(iii) speed
(iv) angular velocity
Answer:
(iii) speed

Question 8.
Name a quantity which remains unchanged during projectile motion.
Answer:
Horizontal component.

Question 9.
What is the effect of air resistance in time of flight and horizontal range?
Answer:
The effect of air resistance is to increase time of flight and decrease horizontal range.

Question 10.
What is the angle between directions of velocity and acceleration at the highest point of trajectory of projectile?
Answer:
At the highest point velocity is horizontal and acceleration is vertical. So angle is 90°.

Question 11.
Can a body have constant velocity and still have a varying speed?
Answer:
No.
If velocity is constant, speed also will be constant.

Question 12.
Can a body have zero velocity, still accelerating?
Answer:
Yes.
When a body is at highest point of motion, its velocity is zero but acceleration is equal to acceleration due to gravity.

Question 13.
A quantity has both magnitude and direction. Is it necessarily a vector? Give an example.
Answer:
No. The given quantity will be a vector only if it obeys laws of vector addition.
Example: Current.

Question 14.
What is the angle between \(\vec{A} \times \vec{B}\) and \(\vec{B} \times \vec{A}\) ?
Answer:
These two vectors will be antiparallel. Hence θ = 180°.

Plus One Physics Motion in a Plane Two Mark Questions and Answers

Question 1.
A particle is projected with a velocity u so that its horizontal range is twice the greatest hieght attained. The horizontal range is
(a) \(\frac{u^{2}}{g}\)
(b) \(\frac{2 u^{2}}{g}\)
(c) \(\frac{4 u^{2}}{5g}\)
(d) None of these
Answer:
(c) Horizontal range, R = \(\frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}\);
Maximum height, H = \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)
As per question, R = 2H

or sin2θ = sin²θ
or 2sinθcosθ = sin²θ or tanθ = 2
Hence, sinθ = \(\left(\frac{2}{\sqrt{5}}\right)\) and cosθ = \(\left(\frac{1}{\sqrt{5}}\right)\)
Horizontal range, R = \(\frac{2 u^{2} \sin \theta \cos \theta}{g}\)

Question 2.

Answer:

Question 3.
Choose the correct alternative given below. A Particle executing uniform circular motion. Then its
(a) Velocity and acceleration are radial.
(b) Velocity and acceleration are tangential.
(c) Velocity is tangential, acceleration is radial.
(d) Velocity is radial, acceleration is tangential.
(e) In a circus, a rider rides in a circular track of radius Y in a vertical plane. The minimum velocity at the highest point of the track will be

• \(\sqrt{2 g r}\)
• \(\sqrt{ g r}\)
• \(\sqrt{3 g r}\)
• 0

Answer:
(c) Velocity is tangential, acceleration is radial.
(e) \(\sqrt{ g r}\)

Question 4.
Two non-zero vectors \(\bar{A}\) and \(\bar{B}\) are such that \(|\bar{A}+\bar{B}|=|\bar{A}-\bar{B}|\). Find the angle between them.
Answer:
\(|\bar{A}+\bar{B}|=|\bar{A}-\bar{B}|\)
|A² + B² + 2ABcosθ| = |A² + B² – 2ABcosθ|
|4ABcosθ| = 0
Since A and B are non-zero we get, cos θ = 0 or θ = 90°.

Question 5.
Consider a particle moving along the circumference of a circle of radius R with constant speed with a time period T.

1. During T, what is the distance coverd and displacement?
2. What is the direction of the velocity at each point?

Answer:

1. Distance = 2πR. Displacement = 0
2. Tangent to the circle at every point.

Question 6.
Classify into scalars and vectors. Frequency, velocity gradient, instantaneous velocity, Area.
Answer:

Scalars	Vectors
Frequency	Instantaneous velocity
Velocity gradient	Ares

Question 7.
A body is projected so that it has maximum range R. What is the maximum height reached during the fight?
Answer:
At maximum range, θ = 45°

Plus One Physics Motion in a Plane Three Mark Questions and Answers

Question 1.
An electron of mass ‘m’ moves with a uniform speed v around the nucleus along a circular radius Y.

1. Derive an expression for the acceleration of the electron.
2. Explain why the speed of electron does not increase even though it is accelerated by the above acceleration.

Answer:
1.

The acceleration is directed towards the centre of the circle and is called centripetal acceleration.
a₀ = \(\frac{v^{2}}{R}\)
But V = Rω
Substituting we get
a_c = Rω²

2. The direction of centripetal force is towards the centre. The angle between force and displacement is 90°. Hence the work done by the centripetal force is zero. So speed does not increase.

Question 2.
A boy pulls his friend in a home made trolley by means of a rope inclined at 30° to the horizontal. If the tension in the rope is 400N.

1. Draw the vertical and horizontal components of tension in the rope.
2. Find the effective force pulling the trolley along the ground.
3. Find the force tending to lift the trolley off the ground.

Answer:
1.

2. Effective horizontal force = T Cos30°
= 400 × Cos 30°

3. Vertical force = T Sin 30°
= 400 × Sin 30°

Question 3.
A stone tied to the end of a string is whirled in a horizontal circle with constant speed.

1. Name the acceleration experienced by the stone.
2. Arrive at an equation for magnitude of acceleration experienced by the stone.

Answer:
1. Centripetal acceleration

2.

The acceleration is directed towards the centre of the circle and is called centripetal acceleration.
a₀ = \(\frac{v^{2}}{R}\)
But V = Rω
Substituting we get
a_c = Rω²

Plus One Physics Motion in a Plane Four Mark Questions and Answers

Question 1.
Two balls are released simultaneously from a certain height, one is allowed to fall freely and other thrown with some horizontal velocity.

1. Will they hit the ground together?
2. At any time during the fall will the velocities of the balls are same?
3. How does the path of the balls appear to a person standing on the ground?

Answer:

1. Both balls will reach at same time.
2. Total velocity of first body and second body is different. First ball has only downward velocity but second ball has both downward and horizontal velocity.
3. The path of first ball appears to be straight line and that of second ball appears to be parabola.

Question 2.
A ball is thrown straight up.

1. Obtain a mathematical expression for the height to which it travels.
2. What js its velocity and acceleration at the top?
3. Draw the velocity-time graph for the ball showing its motion up and down.

Answer:
1. u = u, v = o, a = -g, h = ?
We can find maximum height using the equation
v² = u² + 2as
0 = u² + 2 × – g × H
2gh = u²
H = \(\frac{u^{2}}{2 g}\)

2. Velocity is zero, but it has a acceleration and its value g = 9.8 m/s².

3.

Question 3.

1. Parallelogram law helps to find the magnitude and direction of the resultant of two forces. State the law.
2. For two vectors \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) are acting at a point with an angle a between them, find the magnitude and direction of the resultant vector.
3. What will be the angle between two vectors of equal magnitude for their resultant to have the same magnitude as one of the vectors?

Answer:
1. Law of parallelogram of vectors:
If two vectors acting simultaneously at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram then the diagonal of the parallelogram passing through that point represents the resultant in magnitude and direction.

2.

Consider two vectors \(\vec{A}(=\overrightarrow{O P}) \text { and } \vec{B}(=\overrightarrow{O Q})\) making an angle θ. Using the parallelogram method of vectors, the resultant vector R can be written as,

SN is normal to OP and PM is normal to OS. From the geometry of the figure
OS² = ON² + SN²
but ON = OP + PN
ie. OS² = (OP+PN)² + SN² ______(1)
From the triangle SPN, we get
PN = Bcosθ and SN = Bsinθ
Substituting these values in eq.(1), we get
OS² = (OP + Bcosθ)² + (Bsinθ)²
But OS = R and OP = A
= A² + 2ABcosθ + B²cos²θ + B²sin²θ
² = A² +2 ABcosθ + B²
R = \(\sqrt{A^{2}+2 A B \cos \theta+B^{2}}\)
The resultant vector \(\overrightarrow{\mathrm{R}}\) make an angle a with \(\overrightarrow{\mathrm{R}}\). From the right angled triangle OSN,

But SN = Bsinθ and PN = Bcosθ

3. 120°

Question 4.
A ball of mass m is projected at an angle with the ground and it is found that its kinetic energy at the highest point is 75% of that at the point of projection.

1. Is it a one dimensional or a two-dimensional motion? Why?
2. Find the angle of projection
3. Determine another angle of projection which produces the same range.

Answer:
1. Two-dimensional motion. Projectile has two dimensions.

2. The K.E at highest point
E_k = E cos²θ,
where E = initial K.E
0.75 E = E cos²θ
cos²θ = 0.75 = 3/4
cosθ = \(\sqrt{3} / 2\)
θ = 60°

3. When an object is projected with velocity ‘u’ making an angle θ to with the horizontal direction, the horizontal range will be
R₁ = \(\frac{u^{2} \sin 2 \theta}{g}\) ____(1)
when an object is projected with velocity u making an angle (90° – θ) with the horizontal direction, then horizontal range will be

From eq (1) eq (2), we get R₁ = R₂, which means that we get same horizontal range for two angles θ and (90 – θ).

Question 5.
“The graphical method of adding vectors helps us in visualizing the vectors and the resultant vector. But, sometimes, it is tedious and has limited accuracy”.

1. Name the alternative method of vector addition.
2. Write a mathematical expression to find resultant of two vectors.
3. A particle is moving eastward with a velocity of 5m/s. |f in 10s, the velocity changes by 5 m/s northwards, what is the average acceleration in this time.

Answer:
1. Analytical method of vector addition.

2. R = \(\sqrt{A^{2}+B^{2}+2 A B \cos \theta}\)

3. Change in velocity

Average acceleration

Question 6.

Answer:

Question 7.
A projectile is an object projected into air with a velocity V so that it is moving under the influence of gravity.

1. What is the shape of the path of projectile?
2. As a projectile moves in its path, is there any point along the path where the velocity and acceleration vectors are perpendicular to each other
3. If E is energy with a projectile is projected.

(i) What is the Kinetic energy at the highest point.
(ii) What is P.E at highest point?

Answer:
1. Parabola

2. Yes, highest point

3. Energy with a projectile is projected:
(i) Kinetic energy E_k = 1/2mv²
Velocity at the highest point = Vcosθ
∴ K.E. at highest point = 1/2m(Vcosθ)²
= 1/2 mv²cos²θ
K.E. = E_k cos²θ

(ii) Potential energy at highest point,
P.E. = mgh
= mg\(\frac{v^{2} \sin ^{2} \theta}{2 g}\) = 1/2mv²sin²θ
P.E. = E_k sin²θ.

Plus One Physics Motion in a Plane Five Mark Questions and Answers

Question 1.
An object is projected with velocity U at an angle θ to the horizontal.

1. Obtain a mathematical expression for the range in the horizontal plane.
2. What are the conditions to obtain maximum horizontal range?
3. Find the maximum height of the object when its path makes an angle of 30° with the horizontal (velocity of projection = 8 ms^-1)

Answer:
1. If we neglect the air resistance, the horizontal velocity (ucosθ) of projectile will be a constant. Hence the horizontal distance (R) can be found as
R = horizontal velocity × time of flight

2. when θ = 45° we get maximum horizontal range

3. Height H

Question 2.
The path of projectile from A is shown in the figure. M is the mass of the particle.

When the particle moves from A to M.

1. a) What is the change in vertical velocity?
2. b) What is the change in speed?
3. What is the change in linear momentum?
4. The ceiling of a long hall is 25m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 ms^-1 can go without hitting the ceiling of the hall?

Answer:
1.

When the particle reaches at M, the vertical component of velocity becomes zero.
change in vertical velocity = u sinθ – 0
= u sinθ

2. change in speed = u cosθ – u

3. change in momentum = mu sinθ – 0
= mu sinθ

4.

θ = 33°48¹
The horizontal range of the ball is

Question 3.
A particle moving uniformly along a circle, experiences a force directed towards the centre and an equal and opposite force directed away from the centre.

1. Name the two forces directed towards and away from the centre.
2. Obtain an expression for the force directed towards the centre.
3. An aircraft executes a horizontal loop at a speed of 720 km hr^-1 with its wings banked at 15°. What is the radius of the loop?

Answer:
1. centripetal force and centrifugal force.

2.


force which produces this centripetal acceleration is called centripetal force.
Centripetal force can be written as F = ma.
F = m\(\frac{V^{2}}{R}\)

3. Speed of aircraft, 720 × \(\frac{5}{18}\) = 200 m/s
The velocity of aircraft, ν = \(\sqrt{r g \tan \theta}\)

Question 4.
A body is projected with a velocity ‘u’ in a direction making an angle θ with the horizontal.

1. Derive the mathematical equation of the path followed.
2. Draw the velocity-time graphs for the horizontal and vertical components of velocity of the projectile.
3. Obtain an expression for the time of flight of the projectile.

Answer:
1. The vertical displacement of projectile at any time t, can be found using the formula.
S = ut + 1/2at²
y = usinθt – 1/2gt²
But we know horizontal displacement,
x = ucosθxt

In this equation g, θ and u are constants. Hence eq.(4) can be written in the form
y = ax + bx²
where a and b are constants. This is the equation of parabola, ie. the path of the projectile is a parabola.

2.

3. The time taken by the projectile to cover the horizontal range is called the time of flight.
Time of flight of projectile is decided by usinθ. The time of flight can be found using the formula s = ut + 1/2 at²
Taking vertical displacement s = 0, a = -g and initial vertical velocity = usinθ, we get
0 = usinθt – 1/2gt²
1/2 gt² = usinθt
t = \(\frac{2 u \sin \theta}{g}\).

Question 5.
An object projected into air with a velocity is called a projectile.

1. What will be the range when the angle of projections are zero degrees and ninety degrees?
2. Show that fora projectile, the upward time of flight is equal to the downward time of flight.
3. At what angles will a projectile have the same range fora velocity?

Answer:
1. When θ = 0°
R = 0
When θ = 90°

2. Upward motion
u = u sinθ, a = -g, v = 0
V = u + at
0 = u sinθ + ^–gt
t_a = \(\frac{u \sin \theta}{g}\) ____(1)
Downward motion
u = 0, V= u sinθ, a = +g
V = u + at
u sinθ = 0 + gt
t_a = \(\frac{u \sin \theta}{g}\) ____(2)
eq (1) and (2), shows up ward time of flight is equal to downward time of flight.

3. θ, 90 – θ.

Question 6.
“An object that is in flight after being thrown or projected is called a projectile”.
1. Which of the following remains constant throughout the motion of the projectile?
(i) Vertical component of velocity
(ii) Horizontal component of velocity
2. Derive an expression for maximum range of a projectile.
3. Show that range of projection of a projectile for two angles of a projection a and (3 is same where α + β = 90°.

Answer:
1. (ii)

2. If we neglect the air resistance, the horizontal velocity (ucosθ) of projectile will be a constant. Hence the horizontal distance (R) can be found as
R = horizontal velocity × time of flight

3. Range of projectile R = \(\frac{\mathrm{u}^{2} \sin 2 \theta}{\mathrm{g}}\)
Case – 1
at angle α,
R_α = \(\frac{\mathrm{u}^{2} \sin 2 \alpha}{\mathrm{g}}\) ____(1)
Case – 2
at an angle β,

From (1) and (2), we get
R_α = R_β

Question 7.
A bullet is fired with a velocity ‘u’ at an angle ‘θ’ with the horizontal such that it moves under the effect of gravity.

1. What is the nature of its trajectory.
2. Arrive at an expression for time of flight of the bullet.
3. What is the relation between time of ascent and time of decent, when air resistance is neglected.
4. How the relation is affected when air resistance . is considered.

Answer:
1. Parabola

2. The time taken by the projectile to cover the horizontal range is called the time of flight. Time of flight of projectile is decided by usinθ. The time of flight can be found using the formula s = ut + 1/2 at²
Taking vertical displacement s = 0, a = -g and initial vertical velocity = usinθ, we get
0 = usinθt – 1/2gt²
1/2 gt² = usinθt
t = \(\frac{2 u \sin \theta}{g}\).

3. Time of ascent = time of descent

4. Time of descent > time of ascent

Plus One Physics Motion in a Plane NCERT Questions and Answers

Question 1.
State for each of the following physical quantities, if it is a scalar or a vector:
Volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
Answer:

• Scalars: Volume, mass, speed, density, number of moles and angular frequency.
• Vectors: acceleration, velocity, displacement, and angular velocity.

Question 2.
Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
Answer:
Work, current.

Question 3.
State, with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

1. Adding any two scalars.
2. Adding a scalar to a vector of the same dimensions
3. Multiplying any vector by any scalar
4. Multiplying any two scalars
5. Adding any two vectors
6. Adding a component of a vector to the same vector.

Answer:

1. No. Scalars must represent same physical quantity.
2. No. Vector can be added only to another vector.
3. Yes. When a vector is multiplied by any scalar, we get a vector.
4. Yes. In multiplication, scalars may not represent the same physical quantity.
5. No. The two vectors must represent the same physical quantity.
6. Yes. The vector and its component must have the same dimensions.

Question 4.
Pick out the only vector quantity in the following list: temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
Answer:
Impulse.

Question 5.
Read each statement below carefully and state with reasons, if it is true or false:

1. The magnitude of a vector is always a scalar.
2. Each component of a vector is always a scalar.
3. The total path length is always equal to the magnitude of the displacement vector of a particle.
4. The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time.
5. Three vectors not lying in a plane can never add up to give a null vector.

Answer:

1. True
2. False
3. False
4. True
5. True.

In order to give a null vector, the third vector should have the same magnitude and opposite direction to the resultant of two vectors.

Question 6.
A cyclist starts from the centre O of a circular park, then cycles along the circumference, and returns to the centre along QO as shown. If the round trip takes 10 minute, what is the

1. Net displacement.
2. Average velocity and
3. Average speed of the cyclist?

Answer:
1. Since both the initial and final positions are the same therefore the net displacement is zero.

2. Average velocity is the ratio of net displacement and total time taken. Since the net displacement is zero therefore the average velocity is also zero.

3. Average Speed

Question 7.
A passenger arriving in a new town wishes to go from the station to hotel located 10km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 minute, what is

1. The average speed of the taxi
2. The magnitude of average velocity? Are the two equal?

Answer:
Magnitude of displacement = 10km
Total path length = 23km
Time taken = 28 min

Average Speed = \(\frac{23 \mathrm{km}}{\frac{7}{15} \mathrm{h}}\)
= 49.3 kmh^-1
Magnitude of average velocity

Students can Download Chapter 1 Nature and Purpose of Business Notes, Plus One Business Studies Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

Kerala Plus One Business Studies Notes Chapter 1 Nature and Purpose of Business

Contents

• Economic and non-economic activities
• Business and its characteristics
• Business, Profession and Employment
• Classification of business activities
• Industry and commerce
• Objectives of business
• Business risk
• Factors to be considered before starting a business.

Activities which human beings undertake are known as human activities. We can divide these activities into two categories.

1. Economic activities
2. Non-economic activities

1. Economic Activities:
The human activities that are undertaken with an objective to earn money or livelihood is known as economic activities. eg: A worker working in a factory, a doctor operating in his hospital, a manager working in the office, a teacher teaching in a school etc.

2. Non-economic activities:
Activities are undertaken to derive psychological satisfaction are known as non economic activities. eg: Mother preparing food for her children, Praying, listening to radio or watching television, playing football with friends, etc.

Types of economic activities:

• Business
• Employment
• Profession

Business:
Business may be defined as an economic activity involving the production or purchase and sale of goods and services with the main object of earning profit by satisfying human needs in the society.
Characteristics of business

1. Business is an economic activity with the object of earning profit.
2. Business includes all the activities concerned with the production or procurement of goods and services.
3. There should be sale or exchange of goods and services for the satisfaction of human needs.
4. Business involves dealings in goods or services on a regular basis. Normally, one single transaction of sale or purchase is not treated as business.
5. One of the main objectives of business is to earn maximum profit.
6. Business involves risk and uncertainty of income. Risk means the possibility of loss due to change in consumer taste and fashion, strike, lockout competition, fire, theft etc.

Employment:
Employment refers to that type of economic activity in which people engage in some work for others regularly and get salary or wages in return of their services.
Characteristics of Employment

1. There must exist employer-employee relationship.
2. There must be a service contract between the employer and employee.
3. Employees get salary or wages for their services
4. Regularity in service.

Profession:
Profession refers to an occupation which requires specialized knowledge, skip and training. Its objective is to provide service to the society.
Characteristics of Profession

1. A profession requires specialized knowledge, training and skill
2. The membership of a professional body is a must
3. Professionals have a code of conduct
4. They charge fee in return of their service.

Comparison of Business, Profession and Employment:

Classification of Business Activities: Business activities may be classified into two categories

• Industry
• Commerce.

Chart showing business activities

Industry:
Industry refers to economic activities, which are connected with conversion of resources into useful goods. Industries may be divided into 3 categories.
They are
1. Primary industries:
Primary industries are connected with the extraction and production of natural resources and reproduction and development of living organisms, plants, etc. Such industries are further divided into two.
(i) Extractive industries:
These industries extract products from natural resources. eg: mining, farrqing, hunting, fishing etc.

(ii) Genetic industries:
These industries are engaged in activities like rearing and breeding of animals, birds and plants. eg: diary faming, paultry farming, floriculture, pisciculture etc.

2. Secondary industries:
Secondary industries deal with materials extracted at the primary stage. Such goods may be used for consumption or for further production. Secondary industries are classified into two.
They are:
(i) Manufacturing industries:
Manufacturing industries engage in converting raw materials into finished goods. eg: Conversion of rubber into cotton, timber into furniture rubber into tyres etc. Manufacturing industries may be further divided into four categories. They are,

• Analytical industry which analyses and separates different elements from the same materials. eg: Oil refinery
• Synthetical industry which combines various ingredients into a new product. eg: cement
• Processing industry which involves successive stages for manufacturing finished products. eg: Sugar and paper industry.
• Assembling industry which assembles different component parts to make a new product. eg: television, car, computer, etc.

(ii) Construction industries:
These industries are involved in the construction of buildings, dams, bridges, roads etc.

3. Tertiary industries:
These are concerned with providing support services to primary and secondary industries. eg: Transport, banking, insurance, warehousing, communication, advertising etc.

Commerce:
Commerce is defined as all activities involving the removal of hindrances in the process of exchange of goods. It includes all those activities, which are necessary for the free flow of goods and services from the producer to the consumer. Commerce includes trade and auxiliaries to trade.
Commerce = Trade + auxiliaries to trade
Functions of commerce:

Various Hindrances	Remedies
Hindrance of person	Trade
Hindrance of place	Transportation
Hindrance of time	Warehousing
Hindrance of risk	Insurance
Hindrance of knowledge	Advertising
Hindrance of finance	Banking

Trade:
Trade refers to sale, transfer or exchange of goods. Trade may be classified into two broad categories
They are:

1. Internal trade
2. External trade

1. Internal, domestic ot dome trade:
is concerned with the buying and selling of goods and services within the geographical boundaries of a country. This may further be divided into two. They are:-
(a) Wholesale trade:
Under wholesale trade, the trader purchases goods in large quantities from the producers, and sells them in smaller quantities to the retailers.

(b) Retail trade:
Under the retail trade, the trader buys in comparatively smaller quantities from the wholesalers or producers and sells them to ultimate consumers.

2. External or Foreign trade:
Foreign trade consists of exchange of goods and services between two or more countries. Foreign trade may be divided in to three.

• Import trade: If goods are purchased from a foreign country, it is called import trade.
• Export trade: When goods are sold to a foreign country, it is known as export trade.
• Entrepot trade: When goods are imported for export to other countries, it is known as entrepot trade.

Auxiliaries to Trade (Aids to trade):
Activities which assist trade are called aids to trade or auxiliaries to trade.

1. Transport & Communication:
Transport facilitates the movement of raw material to the place of production and the finished products from factories to the place of consumption. Communication helps the producers, traders and consumers to exchange information with one another.

2. Banking & Finance:
Banking helps business activities to overcome the problem of finance. Commercial banks lend money in the form of overdraft, cash credit, loans and advances etc… and they also provide many services required for the business activity.

3. Insurance:
The goods may be destroyed while in production process or in transit due to accidents, or in storage due to fire or theft, etc. Insurance provides protection in all such cases.

4. Warehousing:
The goods should be stored carefully from the time they are produced till the time they are sold. This function is performed by warehouses.

5. Advertising:
Advertising helps in providing information about available goods and services and create in them a strong desire to buy the product.

Multiple Objectives of Business:
The main objectives of a business are:
1. Market standing:
A business firm can succeed only when it has a good market standing. Market standing refers to the position of an enterprise in relation to its competitors.

2. Innovation:
Innovation means developing new product or services orfinding new ideas and new methods of production and distribution. Innovation accelerates the growth of an enterprise.

3. Productivity:
Productivity is ascertained by comparing the value of output with the value of input. Every enterprise must aim at greater productivity through the best use of available resources.

4. Physical and financial resources:
The business must aim at maximum utilization of available physical and financial resources, i.e. men, material, money and machine in the best possible manner.

5. Earning Profit:
Earning maximum profit is the primary objective of every business. Profit is required for survival and growth of a business.

6. Manager performance and development:
Efficient managers are needed to conduct and co-ordinate business activities. So it is the objective of an enterprise to implement various programs for motivating the managers.

7. Worker performance and attitude:
Every enterprise must aim at improving its workers performance by providing fair salary, incentives, good working conditions, medical and housing facilities.

8. Social responsibility:
It refers to the obligation of business firm to contribute resources for solving social problems and work in a socially desirable manner.

Business Risks:
The term ‘business risks’ refers to the possibility of inadequate profits or even losses due to uncertainties or unexpected events. Business enterprises may face two types of risk, i.e. speculative risk and pure risk.

Speculative risks involve both the possibility of gain as well as the possibility of loss. It arise due to change in demand, change in price etc. Pure risks involve only the possibility of loss or no loss. The chance of fire, theft or strike is examples of pure risks.
Nature of Business Risks:

1. Business risks arise due to uncertainties.
2. Risk can be minimized, but cannot be eliminated. It is an essential part of business.
3. Degree of risk depends mainly upon the nature and size of business.
4. Profit is the reward for risk taking.

Causes of Business Risks: Business risks arise due to a variety of causes.
They are:

1. Natural Causes: it includes natural calamities like flood, earthquakes, lightning, heavy rains, famine, etc.
2. Human Causes: Human causes include dishonesty, carelessness or negligence of employees, strikes, riots, management inefficiency, etc.
3. Economic causes: These include change in demand, change in price, competition, technological changes etc.
4. Political Causes: Change in Govt, policies, taxation, licensing policy etc.

Starting a Business – Basic Factors:
Factors to be considered for starting a business:
1. Selection of line of business:
The first thing to be decided by any entrepreneur of a new business is the nature and type of business to be undertaken.

2. Size of the firm:
If the market conditions are favorable, the entrepreneur can start the business at a large scale. If the market conditions are uncertain and risks are high, a small size business would be better choice.

3. Choice of form of ownership:
The selection of a suitable form of business enterprise i.e. Sole proprietorship, Partnership or a Joint stock company is an important management decision. It depends on factors like nature of business, capital requirements, liability of owners, legal formalities, continuity of business etc.

4. Location of business enterprise:
Availability of raw materials and labour, power supply and services like banking, transportation, communication, warehousing, etc., are important factors while making a choice of location.

5. Financing:
Proper financial planning must be done to determine (a) the requirement of capital, (b) source from which capital will be raised and (c) the best ways of utilizing the capital in the firm.

6. Physical facilities:
Availability of physical facilities including machines and equipment, building and supportive services is a very important factor to be considered at the start of the business.

7. Plant layout:
Layout means the physical arrangement of machines and equipment needed to manufacture a product.

8. Competent worked force:
Every enterprise needs competent and committed employees to perform various activities so that physical and financial resources are converted into desired outputs.

9. Tax planning:
The promoter must consider in advance the tax liability under various tax laws and its impact on business decision.