11. Work and Energy Class 9 NCERT Exemplar Solutions Chapter 11 (CBSE Science)
CBSE Class 9 Science Chapter 11: Work and Energy – NCERT Exemplar Questions with Answers
Chapter 11: Work and Energy
Multiple Choice Questions
1. When a body falls freely towards the earth, then its total energy
(a) increases (b) decreases (c) remains constant (d) first increases and then decreases
Answer: (c) remains constant
[ When a body falls freely towards the Earth, its potential energy decreases while its kinetic energy increases by the same amount. Therefore, the total mechanical energy remains constant if air resistance is neglected.]
2. A car is accelerated on a levelled road and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car
(a) does not change (b) becomes twice to that of initial (c) becomes 4 times that of initial (d) becomes 16 times that of initial
Answer: (a) does not change
[ Potential energy depends on the height of the object above the ground. Since the car is moving on a levelled road, its height does not change. Therefore, its potential energy remains unchanged.]
3. In case of negative work the angle between the force and displacement is
(a) 0° (b) 45° (c) 90° (d ) 180°
Answer: (d) 180°
[ Work done is negative when the force acts in the direction opposite to the displacement. In this case, the angle between force and displacement is 180°.]
4. An iron sphere of mass 10 kg has the same diameter as an aluminium sphere of mass is 3.5 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same
(a) acceleration (b) momenta (c) potential energy (d) kinetic energy
Answer: (a) acceleration
[ When two bodies fall freely under gravity, they experience the same acceleration due to gravity, irrespective of their masses. Therefore, both spheres have the same acceleration when they are 10 m above the ground.]
5. A girl is carrying a school bag of 3 kg mass on her back and moves 200 m on a levelled road. The work done against the gravitation al force will be (g =10 m/s² )
(a) 6 ×10³ J (b) 6 J (c) 0.6 J (d) zero
Answer: (d) zero
[ The gravitational force acts vertically downward, while the girl moves horizontally on a levelled road. Since the angle between force and displacement is 90°, the work done against gravitational force is zero.]
6. Which one of the following is not the unit of energy?
(a) joule (b) newton metre (c) kilowatt (d) kilowatt hour
Answer: (c) kilowatt
[ Kilowatt is a unit of power, not energy. It measures the rate of doing work or using energy.]
7. The work done on an object does not depend upon the
(a) displacement (b) force applied (c) angle between force and displacement (d) initial velocity of the object
Answer: (d) initial velocity of the object
[ Work done depends on force and displacement and the angle between them but it does not depend on the initial velocity of the object.]
8. Water stored in a dam possesses
(a) no energy (b) electrical energy (c) kinetic energy (d) potential energy
Answer: (d) potential energy
[ Water stored at a height in a dam has energy due to its position above the ground, which is known as gravitational potential energy.]
9. A body is falling from a height
. After it has fallen a height 
, it will possess
(a) only potential energy (b) only kinetic energy (c) half potential and half kinetic energy (d) more kinetic and less potential energy
Answer: (c) half potential and half kinetic energy
[ When a body falls freely, its potential energy keeps converting into kinetic energy. After falling half the height, half of its initial potential energy becomes kinetic energy, so both are equal.]
Short Answer Questions
10. A rocket is moving up with a velocityv. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies?
Answer: We know that Kinetic energy is
If velocity = v, then the Kinetic energy is 
If velocity = 3v, then the Kinetic energy is
The ratio of two kinetic energies = 
So, the velocity becomes three times, the kinetic energy becomes nine times.
11. Avinash can run with a speed of 8 m/s against the frictional force of 10 N, an d Kapil can move with a speed of 3 m/s against the frictional force of 25 N. Who is more powerful and why?
Solution: We know that , Power = Force × Velocity
P = F × v
For Avinash : Here, v = 8 m/s , F = 10 N
For Kapil : Here, v = 3 m/s , F = 25 N
The power depends on both force and speed and even though Kapil applies more force, Avinash runs at higher speed, so his total power is more.
Avinash is more powerful because he develops higher power (80 W > 75 W).
12. A boy is moving on a straight road against a frictional force of 5 N. After travelling a distance of 1.5 km he forgot the correct path at a round about (Fig. 11.1) of radius 100 m. However, he moves on the circular path for one and half cycle and then he moves forward upto 2.0 km. Calculate the work done by him.
Solution: Here, F = 5 N , 
One full cycle circumference 
m
One and half cycles 
Total distance 
Work done 
13. Can any object have mechanical energy even if its momentum is zero ? Explain.
Answer: Yes, an object can have mechanical energy even if its momentum is zero.
Momentum 
; if 
, then either 
.
If 
, then kinetic energy =0, but the object can still have potential energy.
Mechanical energy = kinetic + potential.
So, the potential energy alone gives nonzero mechanical energy.
14. Can any object have momentum even if its mechanical energy is zero? Explain.
Answer: No, an object cannot have momentum if its mechanical energy is zero.
We know that, mechanical energy = Kinetic energy + Potential energy
If total mechanical energy = 0, and potential energy ≥ 0 , then kinetic energy must be 0.
Kinetic energy = 0 , then
Momentum p = mv . So, .
15. The power of a motor pump is 2 kW. How much water per minute the pump can raise to a height of 10 m? (Given g = 10 m/s² )
Answer: Given, P = 2 kW = 2000 W , h = 10 m , t = 1 minute = 60 second , g = 10 m/s²
We know that, 
The pump can raise 1200 kg of water per minute to a height of 10 m.
16. The weight of a person on a planet A is about half that on the earth. He can jump upto 0.4 m height on the surface of the earth. How high he can jump on the planet A?
Solution: Given, 
, 
On Planet A, weight is half of that on Earth. i.e., 
We have, 
For earth : Here, 
For planet A :
He can jump 0.8 m on Planet A.
17. The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.
Answer: Let a body of mass m move with initial velocity u. A constant force F acts on it through a distance s, and its final velocity becomes v.
We know that ,
From Newton’s Second Law, 
So, 
We have, 
Again, 
Work done = Final kinetic energy − Initial kinetic energy = Increase in kinetic energy .
Thus, the increase in the kinetic energy of the body is equal to the work done by the force on the body.
18. Is it possible that an object is in the state of accelerated motion due to external force acting on it, but no work is being done by the force. Explain it with an example.
Answer: Yes, it is possible. When a force is perpendicular to the direction of motion, it changes only the direction of velocity and not the speed, so work done is zero. Example: In uniform circular motion, the centripetal force acts towards the centre while displacement is tangential, so no work is done but acceleration exists.
19. A ball is dropped from a height of 10 m. If the energy of the ball reduces by 40% after striking the ground, how much high can the ball bounce back? (g = 10 m/s² )
Solution: Given, h = 10 m
Energy loss after hitting ground = 40%
So, energy remaining = 60%
When the ball is at 10 m height, its energy is gravitational potential energy,
Initial energy = m × 10 × 10 = 100m
After striking the ground, the energy reduces by 40%.
Energy left = 100% − 40% = 60% of the original energy.
Original energy (at drop height) = mgh = mg × 10
Energy after bounce = 60% of original = 0.6 × mg × 10 = 6 mg
Let h’ be the height reached by the ball at the maximum bounce.
A/Q, 
The ball will bounce back to a height of 6 metres.
20. If an electric iron of 1200 W is used for 30 minutes everyday, find electric energy consumed in the month of April.
Solution: Here, P = 1200 W = 1.2 kW , T = 30 minutes = 30/60 = 0.5 hours
Energy consumed per day = Power × Time = 1.2 kW × 0.5 h = 0.6 kWh (units) per day
April has 30 days.
Total energy consumed in April = 0.6 kWh/day × 30 days = 18 kWh
Therefore, electric energy consumed in the month of April is 18 units.
Long Answer Questions
21. A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?
Answer: Let, mass of light object = m₁ and mass of heavy object = m₂ (m₂ > m₁)
Both have the same momentum 
So, 
We have that, kinetic energy 
And 
Since m₂ > m₁, therefore 
So, the lighter object has greater kinetic energy.
22. An automobile engine propels a 1000 kg car (A) along a levelled road at a speed of 36 km/h . Find the power if the opposing frictional force is 100 N. Now, suppose after travelling a distance of 200 m, this car collides with another stationary car (B) of same mass and comes to rest. Let its engine also stop at the same time. Now car (B) starts moving on the same level road without getting its engine started. Find the speed of the car (B) just after the collision.
Solution: Given, 
, 
, 
Speed 
Distance before collision = 200 m
We have, 
(b) Let, velocity of car B is 
. Here, 
.
Initial momentum 
kgm/s
Final momentum 
Since car A comes to rest after collision, we apply Law of Conservation of Momentum.
A/Q, 
m/s
Speed of car B just after collision = 10 m/s
So, car B moves with the same speed which car A had before collision.
23. A girl having mass of 35 kg sits on a trolley of mass 5 kg. The trolley is given an initial velocity of 4 m/s by applying a force. The trolley comes to rest after traversing a distance of 16 m. (a) How much work is done on the trolley? (b) How much work is done by the girl?
Solution: Given, Mass of girl = 35 kg , Mass of trolley = 5 kg
Total mass 
, u = 4 m/s , v = 0 m/s (comes to rest) , s = 16 m
(a) Work done 
Therefore, work done on trolley = – 320 J
(b) The girl sits passively on the trolley and applies no external horizontal force herself. Work done by the girl = 0 J .
24. Four men lift a 250 kg box to a height of 1 m and hold it without raising or lowering it.
(a) How much work is done by the men in lifting the box?
(b) How much work do they do in just holding it?
(c) Why do they get tired while holding it? (g = 10 m/s² )
Solution: Given, m = 250 kg , h = 1 m , g = 10 m/s²
(a) Work done by the men in lifting the box 
(b) Here, The displacement (s) = 0 m (The box is not moving)
We know that, Work = force × displacement
So, the men do no work while just holding the box.
(c) They get tired because their muscles continuously use energy to apply force, even though no mechanical work is done.
25. What is power? How do you differentiate kilowatt from kilowatt hour? The Jog Falls in Karnataka state are nearly 20 m high. 2000 tonnes of water falls from it in a minute. Calculate the equivalent power if all this energy can be utilized? (g = 10 m/s² )
Answer: Power is defined as the rate of doing work.
i.e., 
The SI unit of power is the watt (W).
The Difference between Kilowatt and Kilowatt-hour
|
Kilowatt (kW) |
Kilowatt-hour (kWh) |
|
It is a unit of power |
It is a unit of energy |
|
1 kW = 1000 W |
1 kWh = energy used by 1 kW power in 1 hour |
|
It tells how fast energy is used |
It tells how much total energy is used |
Here, h = 20 m , mass of water (m) = 2000 tones 
kg , t= 1 minute = 60 seconds , g = 10 m/s²
The potential energy 
The power 
26. How is the power related to the speed at which a body can be lifted? How many kilograms will a man working at the power of 100 W, be able to lift at constant speed of 1 m/s vertically? (g = 10 m/s² )
Solution: Here, P = 100 W, v = 1 m/s , g =10 m/s²
We have, 
So, basically, at 100 W power, he is able to lift a 10 kg mass straight upward steadily.
27. Define watt. Express kilowatt in terms of joule per second. A 150 kg car engine develops 500 W for each kg. What force does it exert in moving the car at a speed of 20 m/s ?
Answer: One watt is the power when 1 joule of work is done in 1 second.
1 kilowatt = 1000 watt
1 kilowatt = 1000 J/s = 1000 J/s
Here, Mass of car = 150 kg , v = 20 m/s
Power developed = 500 W per kg
We have, P = 150 × 500 W = 75000 W
Again, 
So, the engine applies a force of 3750 newtons while moving the car at 20 m/s.
28. Compare the power at which each of the following is moving upwards against the force of gravity? (given g = 10 m/s² )
(i) a butterfly of mass 1.0 g that flies upward at a rate of 0.5 m/s .
(ii) a 250 g squirrel climbing up on a tree at a rate of 0.5 m/s .
Answer: We have, Power = Force × velocity .
(i) Butterfly : Here, M = 1.0 g = 0.001 kg , g = 10 m/s² , v = 0.5 m/s
We have, 
(ii) Squirrel : Here, M = 250 g = 0.25 kg
We have, 
Thus, the squirrel is moving upwards with 250 times more power than the butterfly ( 
), even though both have the same speed.
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