NCERT Solutions for Class 9 Science Chapter 11 Work and Energy

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’.

1. Suma is swimming in a pond.
2. A donkey is carrying a load on its back.
3. A wind mill is lifting water from a well.
4. A green plant is carrying out photosynthesis.
5. An engine is pulling a train.
6. Food grains are getting dried in the sun.
7. A sailboat is moving due to wind energy.

Answer: Work is said to be done when force is applied on the object or when displacement of body takes place in the the direction of force or opposite to the direction of force.

1. While swimming Suma applies force to move water backward. Here, force causes displacement causing Suma to move in forward direction. Here work is done.
2. When donkey carries load, it applies force in upward direction and displacement is in forward direction. As force is perpendicular to displacement, work done is zero.
3. Windmill lifts water against the gravitational force, thus, work is done by windmill in lifting water.
4. Work done here is zero, as there is no displacement of leaves in the plant.
5. For pulling a train, force is applied by the engine on the train which causes displacement of train in forward direction. Therefore, work is done here.
6. Food grain do not move due to sun rays when dried under the sun. Therefore, in this case work is not done.
7. Force is applied by wind energy which moves the boat in forward direction. Thus, in this case, work is done.

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: Work done due to force of gravity depends on the vertical displacement of the body. Vertical displacement is measured as difference in initial point and final point. Therefore, work done is zero.

Work done by gravity W = mgh .

Vertical displacement h = 0

∴ W = mg x 0 = 0 J

∴ Work done by gravity is zero joules.

3. A battery lights a bulb. Describe the energy changes involved in the process.

Answer: Following process shows the changes involved when battery lights a bulb.

Chemical energy ⟶ Electrical energy ⟶ Light energy ⟶ Heat energy.

When bulb is connected to battery chemical energy from battery is converted to electrical energy. This electrical energy is utilised to light bulb, thereby, converting into heat and light energy.

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 of body m = 20 kg,

Initial velocity of an object = u = 5 m/s

Final velocity of an object = v = 2 m/s

Initial kinetic energy = E_i = ½ mu² = ½ x 20 x (5)² = 10 x 25 = 250 J

Final kinetic energy = E_f = ½ mv² = ½ x 20 x (2)² = 10 x 4 = 40 J

Therefore, work done by force = initial kinetic energy – final kinetic energy = 40 – 250 = – 210 J

Negative sign indicates that force is acting in direction opposite to the object’s motion.

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: Work done by gravitational force is due to the vertical displacement. If object moves from point A to B on the table, no vertical displacement takes place. Therefore, h = 0

W = mgh = mg x 0 = 0

Therefore, work done due to gravity on an object is zero.

6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?

Answer: When body falls freely its potential energy decreases and kinetic energy increases. Therefore decrease in potential energy is equal to increase in kinetic energy. Therefore, total mechanical energy of the body remains conserved. Thus, it does not violates law of conservation of energy.

7. What are the various energy transformations that occur when you are riding a bicycle?

Answer: Muscular energy of person riding bicycle is converted into rotational kinetic energy while pedaling which moves the bicycle. Therefore, bicycle as well as person riding it both have kinetic energy.

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: No energy transfer takes place as rock doesn’t move. Energy spend by the muscles is used up to overcome the moment of inertia of rock.

9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?

Answer: We know that 1 kWh = 3.6 x 106 J and 1 unit = 1 kWh

∴ 250 units of energy = 250 x 3.6 x 10⁶ = 9 x 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 of object = 40 kg

Height h of when object is raised above the ground = 5 m

Therefore, gravitational potential energy is given by ,

W = mgh

= 40 x 5 x 9.8

= 1960 J

Potential energy P.E of an object half way down will be = 1960 / 2 = 980 J =

We know that, decrease in potential energy is equal to increase in kinetic energy therefore, at halfway kinetic and potential energy of an object will be same.

∴ Kinetic energy KE = 980 J

11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

Answer: When satellite moves around the earth, force of gravity acting on the satellite is perpendicular to it’s path of displacement. This show that work done by the satellite is zero.

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 it is possible for an object to carry out displacement in absence of force. This is possible in condition of uniform velocity. Consider an object moving with constant velocity. Here net force acting on an object is zero. But object shows displacement along its path. Therefore, displacement of an object is possible in absence of force.

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: Work is done when force acts on the body and displacement occurs by the body. If a person holds a bundle on hay over his head, then there is no displacement. Thus, no work is done by him.

14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?

Answer: Given: Power of heater = 1500 W or 1.5 kW

Time T = 10 hrs

Energy used by an electric heater is given by ,

P = W / T

Now, work done is same as the energy consumed by the heater.

∴ Energy consumed = P x T

∴ Energy consumed = 1.5 x 10 = 15 kWh

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: Law of conservation of energy states that, “energy can neither be destroyed nor be created, it is converted from one form to another.”

Let’s consider the following situation –

Let P be the mean position and Q and R be the left and right extreme positions of the bob.

When bob is drawn from mean position P to any of the extreme position Q or R, it gains high potential energy. Consider that bob is drawn at position R. When the bob is released from position R it starts moving towards position P. Here the potential energy of the bob decreases and kinetic energy of the bob increases. When bob reaches at position P it has maximum kinetic energy. Now when bob moves toward position Q. Its kinetic energy decreases and potential energy increases. At position Q it has maximum of potential energy. Again coming back to point P its potential energy decreases and kinetic energy increases.

Thus it is concluded that kinetic energy is maximum at mean position and potential energy is maximum at extreme positions.

The bob do not oscillates forever. This is due to resistance offered by air and friction offered from the point of support. Thus, law of conservation of energy is not violated here, this is because energy lost by the pendulum due to friction is absorbed by the surrounding of the pendulum.

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: Following expression shows kinetic energy of an object with mass m and velocity v.

E_k = (½)mv². Therefore, work of (½)mv²should be done on an object to bring it in rest position.

17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?

Answer: Let E_k be the kinetic energy of the car.

It is given that mass m of car is 1500 kg and

Velocity v of the car is 60 km/h or 60 x (1000/ 3600) m/s

V = 60 x 0.277 m/s

= 16.66 m/s

Therefore E_k = ½ mv²

E_k = ½ (1500)(16.66)²

= ½ (1500)(277.77)

= 416666.66 / 2

= 208333.33

≅ 20.83 x 104 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: It is known that work is done when force is applied on the body and displacement is carried in the direction or in opposite direction of the applied force.

Consider case 1 –

Here, force acting on the block is perpendicular to the displacement. Therefore, work done is in this situation is zero.

Case 2 –

Here, the direction of force is same as the direction of displacement. Therefore, work done in this situation is positive.

Case 3 –

Here, the direction of force is opposite to the direction of displacement. Therefore, work done in this situation is negative.

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: Statement given by Soni is right. This happens when all forces acting on an object cancels out each other, thus, total force acting on an object will be zero.

20. Find the energy in kWh consumed in 10 hours by four devices of power 500 W each.

Answer: Given – Power of the device P = 500 W = 0.5 kWh

Time T = 10 hours

We know that, Power P = W / T

Also, energy consumed by the device = work done

∴ Energy consumed by device = W = P x T

∴ Energy consumed = 0.5 x 10 = 5 kWh

Thus, energy consumed by four devices in 10 hours = 4 x 5 = 20 kWh

21. A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?

Answer: When a body falls freely on the ground, its potential energy decreases and kinetic energy increases. As the ball reaches the ground all its potential energy gets converted into kinetic energy. When ball hits the ground, the kinetic energy of the ball gets converted into heat and sound energy.

Check other lessons NCERT Solutions for Class 9

Download free NCERT textbook class 9 Science – Chapter 11 Work and Energy