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Chapter 10: Work and Energy - NCERT Solutions
In-Text Questions (Page No–115)
1. A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 10.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?
Answer - Work done, W = Force × Displacement
Given:
Force, F = 7 N
Displacement, d = 8 m
Since the force acts in the direction of displacement,
W = F × d = 7 × 8 = 56 J
In-Text Questions (Page No–116)
1. When do we say that work is done?
Answer - Work is said to be done when a force is applied on an object and the object gets displaced in the direction of the force.
2. Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Answer - Work done (W) = Force (F) × Displacement (d)
3. Define 1 J of work.
Answer - 1 joule is the amount of work done when a force of 1 newton displaces an object by 1 metre in the direction of the force.
4. A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?
Answer - Given:
Force, F = 140 N
Displacement, d = 15 m
Work done, W = F × d = 140 × 15 = 2100 J
In-Text Questions (Page No–119)
1. What is the kinetic energy of an object?
Answer - The energy possessed by a body due to its motion is called kinetic energy.
2. Write an expression for the kinetic energy of an object.
Answer - Kinetic energy (K.E.) = ½ × m × v², where m is the mass of the object and v is its velocity.
3. The kinetic energy of an object of mass, m moving with a velocity of 5 m/s is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?
Answer - Given:
Initial velocity, v = 5 m/s
K.E. = 25 J

(i) When velocity is doubled (v = 10 m/s):
K.E. ∝ v²
New K.E. = 25 × (10² / 5²) = 25 × (100 / 25) = 100 J

(ii) When velocity is tripled (v = 15 m/s):
New K.E. = 25 × (15² / 5²) = 25 × (225 / 25) = 225 J
In-Text Questions (Page No–123)
1. What is power?
Answer - Power is the rate at which work is done or energy is transferred.
2. Define 1 watt of power.
Answer - 1 watt is the power of an object when 1 joule of work is done in 1 second.
1 W = 1 J / 1 s
3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Answer - Given:
Energy consumed = 1000 J
Time = 10 s

Power = Work / Time = 1000 / 10 = 100 W
4. Define average power.
Answer - Average power is defined as the total work done or total energy consumed divided by the total time taken.
Exercises
1. Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work’. • Suma is swimming in a pond. • A donkey is carrying a load on its back. • A wind-mill is lifting water from a well. • A green plant is carrying out photosynthesis. • An engine is pulling a train. • Food grains are getting dried in the sun. • A sailboat is moving due to wind energy.
Answer -
  • Suma is swimming in a pond: Work is done because her muscles apply force and displacement occurs.
  • A donkey is carrying a load on its back: No work is done by the donkey on the load in the direction of motion because force and displacement are perpendicular.
  • A wind-mill is lifting water from a well: Work is done as the windmill exerts force and water is displaced upwards.
  • A green plant is carrying out photosynthesis: No mechanical work is done as there is no force and displacement involved.
  • An engine is pulling a train: Work is done because the engine applies force and the train moves.
  • Food grains are getting dried in the sun: No mechanical work is done by the grains.
  • A sailboat is moving due to wind energy: Work is done by the wind on the sailboat causing displacement.
2. An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object?
Answer - The work done by gravity is equal to the change in potential energy, which is zero because the initial and final heights are the same.

So, the total work done by gravity = 0 J.
3. A battery lights a bulb. Describe the energy changes involved in the process.
Answer - In this process, chemical energy stored in the battery is converted into electrical energy, which then converts into light energy and heat energy in the bulb.
4. Certain force acting on a 20 kg mass changes its velocity from 5 m/s to 2 m/s. Calculate the work done by the force.
Answer - Given:
Mass, m = 20 kg
Initial velocity, u = 5 m/s
Final velocity, v = 2 m/s

Work done = Change in kinetic energy
= ½ × m × (v² – u²)
= ½ × 20 × (2² – 5²)
= 10 × (4 – 25)
= 10 × (–21) = –210 J

So, work done by the force is –210 J (negative because velocity decreased).
5. A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.
Answer - Since the object is moved horizontally, there is no displacement in the direction of gravitational force.

Work done by gravity = 0 J
6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Answer - No, it does not violate the law of conservation of energy. The decrease in potential energy is exactly equal to the increase in kinetic energy. The total mechanical energy remains conserved.
7. What are the various energy transformations that occur when you are riding a bicycle?
Answer - While riding a bicycle:
Muscular (chemical) energy → Mechanical energy (kinetic energy + sound + some heat due to friction).
8. Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?
Answer - Yes, energy transfer takes place in your body. Even though the rock doesn’t move, your muscular energy gets converted into heat energy, which warms up your body.
9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
Answer - 1 unit = 1 kWh = 1000 × 3600 = 3.6 × 106 J

Energy = 250 × 3.6 × 106 = 9 × 108 J
10. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.
Answer - Given:
Mass, m = 40 kg
Height, h = 5 m
g = 10 m/s²

Potential Energy (PE) = mgh = 40 × 10 × 5 = 2000 J

At half-way (h = 2.5 m):
PE = 40 × 10 × 2.5 = 1000 J

So, KE = Total energy – PE = 2000 – 1000 = 1000 J
11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.
Answer - The work done by the force of gravity on a satellite moving in a circular orbit around the Earth is zero. This is because the force of gravity acts perpendicular to the direction of displacement of the satellite at every point in its circular path. Since work = Force × Displacement × cosθ and θ = 90°, work done = 0.
12. Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your friends and teacher.
Answer - Yes, according to Newton’s First Law of Motion, an object in motion continues to move with the same velocity unless an external force acts on it. So, displacement can occur without any force acting, provided the object was already in motion.
13. A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer.
Answer - No work is done in terms of physics because there is no displacement of the bundle in the direction of the applied force. Work is defined as force × displacement. Although the person gets tired, the energy is used internally in his muscles, not to do mechanical work.
14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Answer - Energy = Power × Time
= 1500 W × 10 h = 1500 × 10 × 3600 J
= 54,00,000 J or 5.4 × 106 J
15. Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?
Answer - When a pendulum is pulled to one side, it gains potential energy. As it is released, potential energy converts into kinetic energy at the mean position. On the other side, kinetic energy again converts into potential energy. This continuous transformation illustrates the law of conservation of energy.

The pendulum eventually comes to rest due to air resistance and friction at the pivot. Its mechanical energy slowly converts into heat and sound. Thus, the total energy is conserved, and it is not a violation of the law of conservation of energy.
16. An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest?
Answer - To bring the object to rest, we must reduce its kinetic energy to zero.

Work done = Change in kinetic energy = ½ × m × v²
17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h.
Answer - Given:
m = 1500 kg, v = 60 km/h = 60 × (1000/3600) = 16.67 m/s

Work done = ½ × m × v²
= ½ × 1500 × (16.67)²
≈ 750 × 278
≈ 2,08,500 J

So, the required work is approximately 2.085 × 105 J
18. In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.
Answer - Sorry, the answer for this question is not available yet. Inconvenience is highly regretted.
19. Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?
Answer - Yes, Soni is right. If all the forces acting on the object cancel each other out (i.e., net force is zero), the object will have zero acceleration. This is based on Newton’s First Law of Motion.
20. Find the energy in joules consumed in 10 hours by four devices of power 500 W each.
Answer - Total Power = 4 × 500 W = 2000 W
Time = 10 h = 36000 s

Energy = Power × Time = 2000 × 36000 = 7.2 × 107 J
21. A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?
Answer - The kinetic energy is converted into heat, sound, and deformation energy when the object hits the ground. The energy is not lost but transformed, in accordance with the law of conservation of energy.