Work, Energy and Power
Solutions for Physics, Class 10, ICSE
Exercise 2A Long Questions
3 questionsAnswer:
(i) When the displacement of the body is in the direction of force then the work done is said to be positive.
Therefore, W = F × S
Example - When a child pushes a toy table then the force applied by the child and the displacement of the table are in the same direction. So, work done is said to be positive.
(ii) When the displacement of the body is in opposite direction to the force applied then the work done is negative.
Therefore, W = – F × S
Example - When a ball is thrown upwards with a force, the balls moves to a height (h).
However, the displacement is opposite to the direction of force of gravity.
W = -mgh
Answer:
When body of mass m falls through a height (h) either vertically or on an inclined plane work is said to be done.
We know, work done is
W = F x S
However, the force of gravity on the body is F = mg acting vertically downwards and the vertical displacement in the direction of force is S = h.
Applying the values of F and S we get,
Work done by the force of gravity is
W = F x S
= m x g x h
Answer:
The two factors on which the power spent by a source depends are :
- The amount of work done by the source
- The time taken by the source to do the said work.
For example:
Let us suppose a man X takes 5 minute to lift a load to the roof of a house and a man Y takes 10 minutes to lift the same load to the roof of the same house.
The work done by both the persons remain the same, but the power spent by the man X is twice the power spent by the man Y because man X does the work faster than man Y.
Exercise 2A Multiple Choice Type
10 questionsAnswer:
Reason — As force F and displacement S are vector quantities and work W is a scalar quantity so work is expressed as a dot product of force and displacement vectors. Hence, we get the expression :
The dot product of two vectors is a scalar.
Answer:
Zero
Reason — When a body revolves in a circular path under the influence of a force, on completing one round the displacement becomes zero, so the work done by the force is W = 0 because work done is a product of force and displacement.
Answer:
-mgh
Reason — When a ball m is thrown upwards to a height h, the displacement h (upwards) is opposite to the direction of force of gravity mg (downwards), so the work done by the force of gravity mg in displacement h is W = -mgh i.e., negative.
A coolie A takes 1 minute to lift a load to the roof of a bus whereas coolie B take 2 minutes to lift the same load to the roof of the same bus. The work done by B is:
- equal to work done by A
- greater than work done by A
- less than work done by A
- none of the above.
Answer:
equal to work done by A
Reason — From formula:
Given that the distance lifted and the force applied are the same for both coolies, as they are lifting the same load to the same height (the roof of the bus) hence, the work done by both coolies is the same.
The time taken to do the work doesn't affect the amount of work done.
A block of mass 20 kg is pulled up a slope as shown in the figure given below with a constant speed by applying a force of 200 N parallel to the slope from the initial position A to the final position B. Work done in moving the block from A to B is:
- 600 J
- 500 J
- 60 J
- 200 J

Answer:
600 J
Reason — Given,
Force = 200 N
Displacement = S = 3 m
As we know,
Work done = force × displacement in the direction of force
Therefore, work done is 600J.
Assertion (A): When the displacement is normal to the direction of force, the work done is zero.
Reason (R): Work done depends on the angle between force and displacement.
- Both A and R are true and R is the correct explanation of A
- Both A and R are true but R is not the correct explanation of A
- assertion is false but reason is true
- assertion is true but reason is false
Answer:
Both A and R are true and R is the correct explanation of A.
Explanation
Assertion (A) is true.
As,
Work done (𝑊) =⋅= Fdcosθ .............(i)
Where
F = magnitude of force
d = displacement
θ = angle between force and displacement
If displacement is normal (perpendicular) to the force, then 𝜃 =
cos = 0 W = 0
Reason (R) is true.
From (i) it is clearly visible that work done depends upon angle between force vector and displacement vector.
Hence, R is the correct explanation of A.
Exercise 2A Numericals
16 questionsAnswer:
Given,
Force = 20 kgf and g = 10N per kg
So,
Force = 20 x 10 = 200 N
Displacement = S = 1 m
As we know,
Work done = force × displacement in the direction of force
(i) When displacement is in the direction of force
Therefore, work done is 200J.
(ii) When displacement is at an angle of 60° with the force
Therefore, work done is 100J.
(iii) When displacement is normal to the force
Therefore, work done is 0.
Answer:
Given,
m = 40 kg
h = 8 m
t = 5 s
(i) Force of gravity acting on the boy
(ii) Work done against gravity
(iii)
Answer:
Given,
mass = 200kgf
height = 2.5m
time = 5s
Force = mg
= 200 x 10 = 2000N
So, we get force is equal to 2000N
(i) Work done = F x h
Therefore, work done is 5000 J.
(ii)
Therefore, power developed by the boy 1000 W.
Answer:
Given,
Force = 750N
height or distance moved = 16 m
time = 5 s
(i) Energy spent or the work done = F x S
Therefore, energy spent is equal to 12000 J
(ii)
Therefore, power spent is equal to 2400 W.
Answer:
Given,
Power of the electric heater = 3kW
Time for which the electric heater is used = 10 hours
We know,
Energy consumed = power × time
(i) Energy consumed in kWh
(ii) Energy consumed in joule.
Answer:
Given,
Volume of water raised = 50 L and
50 L = 50 × 10-3 m3
height = 25m
time spent = 5s
As we know,
Mass of water = Volume of water × density of water
Work done in raising 50 kg water to height of 25 m is
W = mgh
Power = work done / time taken
Substituting the values we get
Therefore, power of the pump is 2500W.
Answer:
Given,
Mass of water = 600kg
Height to which the water has to be raised = 75 m
Time = 10 s
(a) Work done by the pump = mgh
Substituting the values we get,
(b)
Substituting the values we get,
(c)
Given,
Efficiency = 40 %
∴ Power rating of pump = 112.5 kW.
Answer:
Given,
Force = 1000 N
Velocity = 30 m/s
Power = force × velocity
Power = 1000 x 30 = 30,000 W
Therefore, power developed by the ox is 30 kWh
Answer:
We know,
work done = Force × distance moved in direction of force
i.e. W = F × S
Given,
Force = 350 N
Distance covered in 30 steps (S)
S = 30 x 20 cm = 600cm
⇒ S = 6m
Substituting the values of F and S
∴ Work done by boy = 2100J
(ii)
∴ Power spent by boy = 35W
Answer:
(i) We know that work done is a product of force and displacement and is independent of time. Hence both persons A and B will do the same amount of work.
Therefore, ratio of work done by A and B = 1:1
(ii) The power developed by the persons A and B :
We know that Power = work done / time
Work done is same by A and B
Time A took = 20 s
Time B took = 15 s
Therefore, more power is spent by B as B does the work at a faster rate.
Substituting the values in formula we get :
Power = 1 / time
Answer:
(i) We know that work done is a product of force and displacement
W = F x S = mgh
Given,
m1 = 40 kgf
m2 = 30 kgf
t1 = 4 min = 4 x 60 =240 sec
t2 = 3 min = 3 x 60 = 180 sec
h1 = h2 = 30 x 20 = 600 cm = 6 m
Therefore,
Work done by boy : Work done by girl = 4 : 3
(ii) The power developed —
We know that,
Therefore,
Power developed by boy : Power developed by girl = 1:1
A man raises a box of mass 50kg to a height of 2m in 20s, while another man raises the same box to the same height in 50s.
(a) Compare: (i) the work done, (ii) the power developed by them.
(b) Calculate the (i) the work done, (ii) the power developed by each man.
Take g = 10N kg-1.
Answer:
(a)
(i) Work done = force x displacement
Hence, work done is same for both men as both carry 50 kg weight to a height of 2m.
Therefore,
Work done by first man : Work done by second man = 1 : 1
(ii)
Let the work done by both men be W.
Power developed by Man A : Power developed by Man B = 5:2
(b)
(i) As we know,
W = F x S = mgh
(ii) Power developed by Man A
Power developed by Man B
Answer:
(a)
(i) Work done = force x displacement
Work done is same for boy and father as both lift 20 litre water from 20 m deep well.
Work done by boy : Work done by father = 1:1
(ii) Comparing Power developed:
Power developed by boy : Power developed by father = 2:3
(b) Work done = mgh
Given,
density of water = 103kg m -3
To convert, density of water to mass per litre
We know,
1 litre = 1000 cm3
and
1 m3 = 106 cm3
So,
Hence,
20L of water = 20 Kg by mass
height = 20m
Now, substituting the values in the formula for work done we get
W = 20 x 9.8 x 20
= 3.92 kJ
Exercise 2A Short Questions
17 questionsAnswer:
(i) When force is in direction of displacement then work done is given as —
Work done = Force x displacement of the point of application of force in the direction of force.
When,
W = work done
F = force applied
S = displacement of the body then we get,
W = F × S
(ii) When force acts at an angle to the direction of displacement then work done is given as —
Work done = Force x component of displacement in the direction of force.
When,
W = work done
F = force applied
S = displacement of the body then we get,
W = F × S Cos θ
Answer:
The two conditions for the work done to be zero are,
(i) When there is no displacement of the body on application of force
i.e. S = 0 and
(ii) When displacement is normal to the direction of force
i.e. θ = 90° as cos 90° = 0
Answer:
When a body moves in a circular path, no work is said to be done by the body as the force is directed towards the centre of circular path (the body is acted upon by the centripetal force).
At all points the displacement is along the tangent to the circular path, (i.e normal to the direction of the force).
Answer:
When a satellite revolves around the earth in a circular orbit the work done is zero as force of gravity acting on satellite is perpendicular to its displacement.
Answer:
Work done is given by the formula:
W = F × S Cos θ
Coolie Y is moving the load on a frictionless horizontal platform. The force acting on the load is the force of gravity. In case of Coolie Y as the platform is horizontal so the angle between force and displacement is 90°.
Work done by Coolie Y = F × S Cos 90° = F x S x 0 = 0.
Therefore Coolie Y does zero work.
Coolie X is moving the load on a slope. Assuming the angle of slope as θ:
Work done by Coolie X = F × S Cos θ
Therefore, work done by coolie X is more than coolie Y.
Answer:
The S.I unit of work is Joule.
C.G.S unit of work is erg.
Relation between joule and erg:
1 joule = 1N × 1m
As we know, 1 N = 105 dyne and 1 m = 102 cm
Therefore,
1 joule = 105 dyne x 102 cm
⇒ 1 joule = 107 dyne cm
So, 1 joule = 107 erg.
Answer:
Work | Power |
---|---|
Work done is the product of force and displacement produced due to the applied force. | Power is the rate of doing work. |
Work done is independent of time. | Power spent depends on the time in which work is done. |
S.I unit of work is joule (J) | S.I unit of power is watt (W) |
Answer:
Energy | Power |
---|---|
Energy is defined as the capacity of a body to do work. | Power is the rate at which energy is supplied by a body. |
Energy spent is independent of time. | Power depends on the time in which energy is spent. |
S.I unit of energy is joule (J). | S.I unit of power is the watt (W). |
Exercise 2A Very Short Questions
11 questionsA force F acts on a body and displaces it by a distance S in a direction at an angle θ with the direction of force.
(a) Write the expression for the work done by the force.
(b) What should be the angle between force and displacement so that the work done is (i) zero, (ii) maximum?
Answer:
(a) When force acts at an angle θ to the direction of displacement then work done is
W = F × S Cos θ
(b)
(i) For work done to be zero the angle between force and displacement should be equal to 90° as cos 90° = 0
Therefore, product will also be zero.
W = F × S Cos 90° = 0
(ii) For work done to be maximum the angle between force and displacement should be equal to 0° as cos 0° = 1
Therefore, product will also be maximum.
W = F × S Cos 0° = F × S
Answer:
When a body is moved in a direction opposite to the direction of force then work is done against the force acting on the body.
When the displacement of the body due to application of force is in a direction opposite to the force then,
θ = 180°, and
cos 180° = -1
Therefore, Work done = (-) Force x displacement of the body.
Answer:
(a) No, work is not done by the man.
(b) No, work is not done by the coolie.
(c) Yes, work is done by the boy in climbing up the 20 stairs.
Explanation
(a) Work is not done by the man as on pushing the wall, it doesn't move hence, there is no displacement of the wall. Work is defined as the product of force and displacement in the direction of the force. Since there is no displacement, no work is done.
(b) Standing with a box on the head doesn't involve any displacement in the direction of the force of gravity acting on the box. The coolie is not moving the box, nor is there any vertical displacement. Therefore, no work is said to be done.
(c) When the boy climbs stairs, he exerts a force to lift his body against gravity. As he climbs, there is a vertical displacement as he moves from one step to the next. Since there is both force and displacement in the direction of the force (upward against gravity), work is done in this scenario.
Answer:
When a coolie carrying a load moves on a horizontal platform, the force of gravity acting on him is normal to the displacement of the load i.e. the angle between force and displacement of load is 90°.
Work done by Coolie = F × S Cos 90° = F x S x 0 = 0.
Therefore, in this case work done by the force of gravity is zero even though the load gets displaced from its initial position.
Answer:
When a boy of mass m climb up stairs of vertical height h then
(a) Work done by the boy against the force of gravity is
W = FS = mgh
(b) The work done when the boy uses a lift in climbing the same vertical height
W = FS = mgh
Answer:
The energy of atomic particles is measured in electron volt (eV)
1 eV = charge on an electron × 1 volt
⇒ 1 eV = 1.6 x 10-19 coulomb x 1 volt
⇒ 1 eV = 1.6 x 10-19 J
Answer:
(a) Power is the physical quantity measured in terms of horsepower.
(b) The relation between horsepower and S.I. unit of power is 1 horsepower = 746 watt.
Answer:
Yes there are cases when we will see no transfer of energy even on application of force.
Example - When a body moves in circular motion then force acts normal to the displacement of the body then there is no transfer of energy and work done is zero.
Exercise 2B Long Question
5 questionsAnswer:
The potential energy possessed by a body due to the force of attraction of the earth on it, is called the gravitational potential energy.
When a body is placed at a height above the ground then the amount of work done in lifting the body to that height against the force of gravity is called the gravitational potential energy.
When we lift a body of mass m from the ground to a height h.Then, force of gravity (mg) acts on the body acting vertically downward which must be equal to the least upward force F required to lift the body.
Work done = force of gravity (mg) × displacement (h)
⇒ W = mgh
So, the work done on the body is stored in the form of its gravitational potential energy when it is at a height h.
Hence,
Gravitational potential energy U = mgh.
Answer:
When the string of a bow is pulled, the work done is stored in the form of elastic potential energy.
When the string is released to shoot the arrow, the potential energy of the bow changes into the kinetic energy.
The kinetic energy is the same potential energy stored when the string was pulled.
Answer:
When the ball is placed on a compressed spring, the compressed spring has elastic potential energy.
The potential energy of the spring changes into kinetic energy when it is released and as a result it flies.

Answer:
On being thrown upwards, the kinetic energy of the pebble changes to potential energy.
Its kinetic energy is completely converted into potential energy when the pebble reaches its maximum height.
The potential energy is then converted into kinetic energy while coming down and the potential energy is completely converted to kinetic energy when the pebble reaches the ground.
Answer:
When the water falls from the height, the potential energy stored in water at a height changes into the kinetic energy.
On reaching the ground, a part of the kinetic energy of water changes into the heat energy which increases the temperature of the water.
Exercise 2B Multiple Choice Type
14 questionsAnswer:
Gravitational potential energy
Reason — Gravitational potential energy is the energy an object possesses because of its position in a gravitational field. It arises from the gravitational force between the object and the Earth (or another massive body).
Answer:
Elastic potential energy
Reason — When an object is deformed (stretched, compressed, or bent), it stores energy within itself due to the deformation. This energy is called elastic potential energy. It arises from the forces within the object's material that act to restore it to its original shape and size when the deforming force is removed.
Answer:
work done
Reason — According to the work energy theorem, the increase in the kinetic energy of a moving body is equal to work done by a force acting in the direction of the moving body.
Answer:
vibrational kinetic energy
Reason — When a wire clamped at both ends is struck in the middle, it will vibrate back and forth. This motion results in vibrational kinetic energy, as the wire undergoes oscillations about its equilibrium position.
Answer:
both rotational and translational kinetic energy
Reason — When a vehicle is in motion, its wheels are both rotating and translating (moving in a straight line). The motion of the vehicle results in translational kinetic energy, as the vehicle moves forward. Additionally, each wheel is rotating about its axis, so it possesses rotational kinetic energy due to its spinning motion.
Answer:
2000 J
Reason — Given,
Initial velocity = 20 m/s.
Mass = 10 kg
Kinetic Energy =
Substituting we get,
Kinetic Energy = = = 2000 J
Answer:
momentum
Reason — The momentum of an object is given by the product of its mass (m) and velocity (v) represented by :
p = mv
If the velocity is doubled, then the new momentum (p') becomes:
p' = m x 2v = 2(mv) = 2p
So, the momentum gets doubled when the velocity is doubled.
Answer:
light energy to electrical energy
Reason — A photoelectric cell, also known as solar cell, converts light energy (photons) into electrical energy (electrons). When light strikes the surface of the cell, it excites electrons, causing them to be ejected from the material (the photoelectric effect). These ejected electrons can then be collected and used as electric current.
Answer:
chemical energy to kinetic energy
Reason — In a petrol vehicle, the chemical energy stored in the fuel (petrol) is converted into kinetic energy as the vehicle moves. This conversion of chemical energy into kinetic energy occurs through the process of combustion within the engine, where the chemical bonds in the fuel are broken, releasing energy that propels the vehicle forward.
Answer:
nuclear energy changes to electrical energy
Reason — Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts, releasing a significant amount of energy. This energy is in the form of nuclear energy and is used for constructive purposes to produce electrical energy.
Answer:
chemical to electrical
Reason — An electric cell, such as a battery, converts chemical energy stored within it into electrical energy when in use. The chemical reactions occurring within the battery cause a flow of electrons, generating an electric current.
Assertion (A): If momentum of a body increases by 50%, its kinetic energy will increase by 125%.
Reason (R): Kinetic energy is proportional to the square of velocity.
- Both A and R are true and R is the correct explanation of A
- Both A and R are false and R is not the correct explanation of A
- assertion is false but reason is true
- assertion is true but reason is false
Answer:
Both A and R are true and R is the correct explanation of A.
Explanation
Assertion (A) is true. When the momentum of a body increases by 50%, its kinetic energy will increase by 125%.
Let initial momentum be p and kinetic energy be K
If p increases by 50%, the new momentum p' = p + =
Relation between kinetic energy and momentum is given by; K =
So, = = = =
So,
Percentage increase in kinetic energy = x 100
= x 100
= x 100
= x 100
= x 100 = 125%
Hence, kinetic energy will increase by 125%.
Reason (R) is true. Kinetic energy is proportional to the square of velocity, according to the formula: KE = mv2.
Exercise 2B Numericals
23 questionsAnswer:
Given,
Mass of body A and body B = m each
Height HA = h
Height HB = 2h
We know, Gravitational potential energy = mgh
Substituting the values we get,
Hence, ratio of gravitational potential energies of the two bodies = 1 : 2
Answer:
Given,
Mass, m = 1 kg
Height, h = 5 m
Gravitational potential energy = mgh
= 1 × 10 × 5
= 50 J
When the mass hits the ground, its entire Potential energy is converted to Kinetic energy.
Hence, Kinetic energy of mass on hitting the ground = 50 J.
Answer:
Given,
Mass of box = 300 Kg
Gravitational potential energy = 29400 J
We know,
Gravitational potential energy = mgh
Therefore,
Substituting the values in formula we get,
Answer:
Given,
Mass = 10Kg
Fall in height = 20 - 8 = 12m
(i) Loss in potential energy = mg(h1 - h2)
Substituting the vales in formula we get,
Loss in potential energy = 10 x 10 x 12 = 1200 J
(ii) Total energy remains constant for free fall.
Total energy = P.E + K.E
So, at height 20 m, K.E = 0
Therefore total energy = P.E + K.E
Total energy = mgh + 0
= 10 x 10 x 20 = 2000 J
Answer:
Mass = 50 Kgf
Increase in gravitational potential energy = mg(h2 – h1)
= 50 x 10 x (9 - 3)
= 50 x 10 x 6
= 3000 J
Answer:
Given,
Mass = 50 kg
Height = 15 m
Gravitational potential energy = mgh
Substituting the values we get,
Answer:
Given,
Mass = 50 kg
h1 = 0 m
h2 = 15 m
(i) Work done by man = mgh2
Substituting the values we get,
W = 50 x 9.8 x 15 = 7350 J
(ii) Increase in his potential energy = Mg (h2 – h1)
= 50 x 9.8 x (15 - 0)
= 7350 J
A block A, whose weight is 100N, is pulled up a slope of length 5m by means of a constant force F (=100N) as illustrated.

(a) What is the work done by the force F in moving the block A, 5m along the slope?
(b) What is the increase in potential energy of the block A?
(c) Account for the difference in the work done by the force and the increase in potential energy of the block.
Answer:
Given,
F = 100 N
h = 3m
displacement = 5m
We know,
(a) Work done = Force × displacement in the direction of the force
(b) The potential energy gained by the block U = mgh
(c) The difference (200 J) energy is used in doing work against the force of friction between the block and the slope and it will appear as heat energy.
Answer:
Given,
Velocity of first body v1 = v
Velocity of second body, v2 = 2v
As the mass of the two bodies are same and as kinetic energy is directly proportional to the square of the velocity (K α v2)
Hence, ratio of their kinetic energies is
Answer:
We know that,
Let the two bodies be A and B.
Let mass of body A be mA and body B be mB. Let velocity of body A be vA and body B be vB.
Given,
Ratio of masses:
Ratio of K.E.:
∴ Ratio of their velocities = 5:3
Answer:
Given,
Mass = 0.5 kg
Initial velocity = 10 m / s
Final velocity of the ball = 6 m / s
Kinetic energy = × mass × (velocity)2
Substituting the values in the equation we get,
Initial KE = x 0.5 x 102
= x 0.5 x 100
= 0.5 x 50
= 25 J
Final KE = x 0.5 x 62
= x 0.5 x 36
= 0.5 x 18
= 9 J
So, change in the kinetic energy of the ball = 9 J - 25 J = -16J
Hence, there is a decrease in the kinetic energy of the ball by 16J.
Answer:
Given,
mass = 500 g = 0.5 kg
Speed = v = 15 m / s
(i) We know,
Kinetic energy = 1 / 2 × mass × (velocity)2
Substituting the values in the equation we get,
\
(ii) We know,
Momentum = mass × velocity
Substituting the values in the equation we get,
Momentum = 0.5 x 15
= 7.5 kgm/s
Answer:
Given,
Initial Mass = 10 kg and
Final mass = 2 × 10 kg = 20kg
Initial Velocity = 20 m / s
Changed velocity v2 = 20 / 2 = 10 m / s
(i) Initial kinetic energy = 1 / 2 × mass × (velocity)2
(ii) Final kinetic energy
Answer:
Given,
Mass = 1000 kg
From, equation of motion we get
(i) Work done = force x displacement
(ii) Power = work done / time taken
Answer:
Given,
Mass = 20 kg
(a) As there is no displacement of the man, so work done is Zero.
(b) We know,
Work done = Kinetic energy of man = 1 / 2 × mass × (velocity)2
∴ Energy Gained = 90 J
(c) We know,
Potential energy = mgh
Answer:
Given,
Mass = 50 g = 0.05 kg
Velocity = 500 m / s
Distance (S) = 10 cm = 0.1 m
(a) The kinetic energy possessed by the bullet = × mass × (velocity)2
Substituting the values in equation we get,
(b)
∴ Average retarding force offered by target = 62500N
Answer:
Given,
Mass = 0.5 kg
Velocity = 2 m / s
Potential Energy possessed by the spring is equal to the kinetic energy of moving trolley.
Kinetic energy of trolley
∴ Potential energy = Kinetic energy = 1.0 J
Exercise 2B Short Questions
12 questionsAnswer:
The energy possessed by a body at rest due to its position or size and shape is called the potential energy.
Different forms of potential energy are as follows:
(i) Gravitational potential energy — It is the energy possessed by a body due to the force of attraction of the earth.
Example — A stone at a height has gravitational potential energy.
(ii) Elastic potential energy — It is the energy possessed by a body due to the deformed state because of change in its shape and size.
Example — When a spring is compressed it has elastic potential energy.
Answer:
A body possesses potential energy even when it is not in motion.
For example — a stone raised at a height has gravitational potential energy.
Answer:
The work done in lifting a body to a height h is
W = force of gravity (mg) × displacement (h) = mgh
Therefore, this work is stored in the body in the form of its gravitational potential energy.
Hence, Gravitational potential energy U = mgh
Answer:
Mass = m
Change in velocity from u to v, so acceleration acts (a)
Force = f
Work done by the force = force × displacement
From equation of motion we know,
Substituting it in the formula for work done:
Answer:
Kinetic energy (KE) and momentum (p) are related as
As both masses have the same momentum p. The kinetic energy k is inversely proportional to the mass of the body.
Hence, a body of light mass has more kinetic energy as smaller the mass, larger is its kinetic energy.
Answer:
The three forms of kinetic energy are:
(i) Vibrational kinetic energy
Example — A wire clamped at both the ends vibrates when struck.
(ii) Rotational kinetic energy
Example — A spinning top.
(iii) Translational kinetic energy
Example — A car moving in a straight path.
Answer:
Potential energy | Kinetic energy |
---|---|
It is the energy possessed by a body due to its changed position or change in shape or size. | It is the energy possessed by a body due to its state of motion. |
It does not depend on the speed of the body. | It depends on the speed of the body. |
Answer:
While transforming energy from one from to another desired form, the entire energy does not change into the desired form. A part of energy changes either to some other undesirable form (usually heat due to friction) or a part is lost to the surroundings due to radiation and becomes useless. This conversion of energy to the undesirable form is called dissipation of energy.
Since, this part of energy is not available to us for any productive purpose so we call this part of energy as degraded energy.
Answer:
While transforming energy from one from to another desired form, the entire energy does not change into the desired form. A part of energy changes either to some other undesirable form (usually heat due to friction) or a part is lost to the surroundings due to radiation and becomes useless. This conversion of energy to the undesirable form is called dissipation of energy or degradation of energy.
Since, this part of energy is not available to us for any productive purpose so we call this part of energy as degraded energy.
Example — When a vehicle is run by using the chemical energy of its fuel a major part is wasted as heat and sound. Only a part of it is changed into useful mechanical energy.
Exercise 2B Very Short Questions
10 questionsAnswer:
(a) A moving cricket ball posses Kinetic energy — K.
(b) A compressed spring posses Potential energy — U.
(c) A moving bus posses Kinetic energy — K.
(d) A stretched wire posses Potential energy — U.
(e) An arrow shot out of a bow posses Kinetic energy — K.
(f) A piece of stone placed on the roof posses Potential energy — U.
Answer:
(a) The expression for a body of mass m moving with a velocity v is given by
(b) 2K / v2 = Joules / (ms-1)2 = kg
So, Kg is the unit of mass
Answer:
Kinetic energy and momentum are related as
Since,
the kinetic energy of both bodies are same, momentum is directly proportional to the square root of mass.
As we can see that mass of body B is greater than that a body A.
Therefore, body B will have more momentum than body A.
Complete the following sentences
(a) The kinetic energy of a body is the energy by virtue of its ...............
(b) The potential energy of a body is the energy by virtue of its ...............
(c) The conversion of part of energy into an undesirable form is called ...............
Answer:
(a) The kinetic energy of a body is the energy by virtue of its motion.
(b) The potential energy of a body is the energy by virtue of its position.
(c) The conversion of part of energy into an undesirable form is called degradation of energy.
Energy can exist in several forms and may change from one form to another. For each of the following, state the energy changes that occur in:
(a) the unwinding of a watch spring
(b) a loaded truck when started and set in motion
(c) a car going uphill
(d) photosynthesis in green leaves
(e) charging of a battery
(f) respiration
(g) burning of a match stick
(h) explosion of crackers
Answer:
(a) Potential energy of a watch spring converts into kinetic energy
(b) Chemical energy of diesel or petrol converts into mechanical energy
(c) Kinetic energy converts into potential energy
(d) Light energy converts into chemical energy
(e) Electrical energy converts into chemical energy
(f) Chemical energy converts into heat energy
(g) Chemical energy converts into heat and light energy
(h) Chemical energy converts into heat, light and sound energy
State the energy changes in the following cases while in use:
(a) Loudspeaker
(b) A steam engine
(c) Microphone
(d) Washing machine
(e) A glowing electric bulb
(f) Burning coal
(g) A solar cell
(h) Biogas burner
(i) An electric cell in a circuit
(j) A petrol engine of a running car
(k) An electric iron
(l) A ceiling fan
(m) An electromagnet.
Answer:
(a) Electrical energy changes into sound energy
(b) Heat energy changes into mechanical energy
(c) Sound energy changes into electrical energy
(d) Electrical energy changes into mechanical energy
(e) Electrical energy changes into light energy
(f) Chemical energy changes into heat energy
(g) Light energy changes into electrical energy
(h) Chemical energy changes into heat energy
(i) Chemical energy changes into electrical energy
(j) Chemical energy changes into mechanical energy
(k) Electrical energy changes into heat energy
(l) Electrical energy changes into mechanical energy
(m) Electrical energy changes into magnetic energy
Answer:
It is not possible to completely convert one form of energy into other as a part of the energy is dissipated in the form of heat which is lost to the surroundings.
Exercise 2C Long Questions
2 questionsShow that the sum of kinetic energy and potential energy (i.e., total mechanical energy) is always conserved in the case of a freely falling body under gravity (with air resistance neglected) from a height h by finding it when
(i) the body is at the top,
(ii) the body has fallen a distance x,
(iii) the body has reached the ground.
Answer:

We know that,
Kinetic energy + potential energy = constant
So, when a body falls from a height h under free fall
(i) At the position A — height h
Initial velocity = 0
Kinetic energy K = 0
Potential energy U = mgh
As, Total energy = KE + PE
Total energy = 0 + mgh
Total energy = mgh (1)
(ii) At the position B — when it has fallen a distance x.
Then, velocity at B = v1
Then u = 0, s = x, a = g
From equation of motion:
v2 = u2 + 2aS
v12 = 0 + 2gx = 2gx
∴ Potential energy U = mg (h – x)
Hence, total energy = K + U = mgx + mg (h – x) = mgh
Total energy = mgh (2)
(iii) At position C (on the ground) —
Let the velocity acquired by the body on reaching the ground be v2.
Then u = 0, s = h, a = g
We know,
v2= u2 + 2aS
v22 = 0 + 2gh
v22 = 2gh
And potential energy U = 0 (at the ground when h = 0)
So, total energy = K + U = mgh + 0
Total energy = mgh (3)
Thus, from equation (1), (2) and (3) we note that the total mechanical energy i.e. the sum of kinetic energy and potential energy always remain constant at each point of motion and it is equal to the initial potential energy at height h.
Answer:

The kinetic energy decreases and the potential energy becomes maximum at B.
After a moment the the to and fro movement starts again.
So, from B to A, again the potential energy changes into kinetic energy and this process repeat again and again.
So, when the bob in its state of to and from movement it has potential energy at the extreme position B or C and kinetic energy at resting position A.
It has both the kinetic energy and potential energy at an intermediate position.
However, the sum of kinetic and potential energy remain same at every point of movement.
Exercise 2C Multiple Choice Type
8 questionsAccording to the principle of conservation of mechanical energy :
- Potential energy of a system is always greater than its kinetic energy
- Kinetic energy of a system is always greater than its potential energy
- Mechanical energy is always converted into heat energy
- Total mechanical energy of a system remains constant if no external force is worked on it.
Answer:
Total mechanical energy of a system remains constant if no external force is worked on it.
Reason — The conservation of mechanical energy states that the total mechanical energy (sum of kinetic energy and potential energy) of a system remains constant if no external forces, such as friction or air resistance, are acting on it.
Answer:
It remains constant
Reason — As the skater glides across the ice, he possess kinetic energy due to his movement. The potential energy remains constant as there is no significant change in height. Assuming a smooth ice surface with no friction or air resistance, the external forces are absent, hence, according to the principle of conservation of mechanical energy, the total mechanical energy (KE + PE) of the skater remains constant.
Answer:
It remains constant
Reason — When the spring is compressed, it stores potential energy. Upon release, this potential energy is converted into kinetic energy as the spring propels an object forward. Assuming there are no significant external forces acting on the system (such as friction), the total mechanical energy of the system remains constant.
A ball of mass m is thrown vertically up with an initial velocity so as to reach a height h. The correct statement is:
- Potential energy of the ball at the ground is mgh.
- Kinetic energy of the ball at the ground is zero.
- Kinetic energy of the ball at the highest point is mgh.
- Potential energy of the ball at the highest point is mgh.
Answer:
Potential energy of the ball at the highest point is mgh.
Reason — At the highest point, the ball has maximum potential energy. The potential energy at a height h, above the ground is given by the formula mgh.
Answer:
mechanical energy
Reason — Mechanical energy, which is the sum of kinetic and potential energy, remains constant during the motion of the body. Initially, when the body is released from a height, it has potential energy. As it falls, this potential energy decreases while its kinetic energy increases. However, the sum of kinetic and potential energy (mechanical energy) remains constant in the absence of external forces like air resistance.
A pendulum is oscillating on either side of its rest position. The correct statement is :
- It has only the kinetic energy at its each position.
- It has the maximum kinetic energy at its extreme position.
- It has the maximum potential energy at its mean position.
- The sum of its kinetic energy and potential energy remains constant throughout the motion.
Answer:
The sum of its kinetic and potential energy remains constant throughout the motion.
Reason — The sum of kinetic and potential energy does not remain constant throughout the motion of a pendulum. It varies as the pendulum swings due to the interconversion of kinetic and potential energy. However, the sum of kinetic and potential energy is constant if we consider the entire system (kinetic energy + potential energy = mechanical energy), as long as there are no external forces like friction acting on the pendulum.
A simple pendulum while oscillating rises to a maximum vertical height of 7 cm from its rest position where it reaches its extreme position on one side. The mass of the bob of simple pendulum is 400 g and g = 10 m/s2. The total energy of the simple pendulum at any instant while oscillating is:
- 0.28 J
- 2.8 J
- 28 J
- 28000 J
Answer:
0.28 J
Reason — Given,
m = 400 g = 0.4 kg
g = 10 m/s2
h = 7 cm = 0.07 m
The potential energy of the pendulum at its extreme position (maximum height) is : mgh
and kinetic energy at this point = 0
Substituting we get,
Total energy = PE + KE = mgh + 0 = (0.4 x 10 x 0.07) + 0 = 0.28 J
Assertion (A): When a hammer is made to fall on a nail fixed upright on a wooden piece, the nail begins to penetrate the wood.
Reason (R): As the hammer starts falling, its kinetic energy begins to change into potential energy.
- Both A and R are true and R is the correct explanation of A
- Both A and R are true and R is not the correct explanation of A
- assertion is false but reason is true
- assertion is true but reason is false
Answer:
assertion is true but reason is false.
Explanation
Assertion (A) is true. When a hammer is made to fall on a nail fixed upright on a wooden piece, the nail begins to penetrate the wood due to the force applied by the falling hammer.
Reason (R) is false. The statement about the conversion of kinetic energy into potential energy as the hammer falls is incorrect. Potential energy is the energy that is stored in an object due to its position above the earth's surface. Hence, when a hammer is lifted it stores potential energy in it and when the hammer starts falling, this potential energy begins to change into kinetic energy and is used in driving a nail into the wood.
Exercise 2C Numericals
8 questionsAnswer:
Given,
Mass = 0.20 kg
Initial velocity = 20ms-1
We know,
Maximum potential energy at the maximum height = initial kinetic energy
Substituting the values in the equation
∴ Maximum potential energy at the maximum height = Initial kinetic energy = 40 J
Answer:
Mass = 500g
Velocity = 15ms-1
(a) We know,
Potential energy at maximum height = initial kinetic energy
mgh = mv2
Substituting the values in the equation we get,
∴ Potential energy at maximum height = Initial kinetic energy = 56.25J
(b) As we know that,
Kinetic energy on reaching the ground = potential energy at the greatest height
= 56.25J
(c) Total energy at its halfway point = (K + U) = 56.25J
A metal ball of mass 2kg is allowed to fall freely from rest from a height of 5m above the ground.
(a) Taking g = 10ms-2, calculate:
(i) the potential energy possessed by the ball when it is initially at rest.
(ii) the kinetic energy of the ball just before it hits the ground?
(b) What happens to the mechanical energy after the ball hits the ground and comes to rest?
Answer:
Given,
Mass = 2 kg
Height = 5m
(a)
(i) the potential energy possessed by the ball when it is initially at rest = mgh = 2 x 10 x 5 = 100J
(ii) As we know that,
The kinetic energy of the ball just before hitting the ground = initial potential energy = mgh = 2 x 10 x 5 = 100J
(b) Mechanical energy of the ball gets converted into heat and sound energy after the ball hits the ground and comes to rest.
Answer:
As the person swings on a rope from a cliff of height h = 20 m then potential energy at the top gets converted into kinetic energy at the lowest point.
From conservation of energy,
Potential energy at top = Kinetic energy at lowest point
mgh = mv2
gh = v2
10 x 20 = v2
400 = v2
m/s
∴ The person is moving at a speed of 20 m/s at the lowest point of the swing.
The diagram given below shows a ski jump. A skier weighing 60kgf stands at A at the top of ski jump. He moves from A and takes off for his jump at B.

(a) Calculate the change in the gravitational potential energy of the skier between A and B.
(b) If 75% of the energy in part (a) becomes the kinetic energy at B, calculate the speed at which the skier arrives at B.
(Take g = 10 ms-2).
Answer:
Given,
Mass = 60 kg
(a)
(b) When kinetic energy at B is 75% of (3.6 × 104)
Since,
Kinetic energy = mv2
Substituting the values in equation we get,
∴ The speed at which the skier arrives at B = 30ms-1
A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce power output of 1MW. (Take g = 10 m s-2).
Answer:
Given,
Efficiency = 40%
Work done = 40% of potential energy
Hence,
Mass of water which must flow through the turbine = 5000Kg
Answer:
Given,
Energy lost = 0.6 x KE
KE = x mass x velocity2
Substituting the values we get,
Amount of energy lost,
Amount of energy available,
Applying the rule for the conservation of energy we get,
Kinetic energy available = potential energy
∴ Maximum vertical height reached = 0.5m
The figure alongside shows a simple pendulum of mass 200 g. It is displaced from the mean position A to the extreme position B. The potential energy at position A is zero. At position B the bob is raised by 5 m.

(a) What is the potential energy of the pendulum at position B ?
(b) What is the total mechanical energy at point C?
(c) What is the speed of the bob at position A when released from position B ? (Take g = 10 ms-2)
Answer:
Given,
h = 5 m, m = 200 g = 0.2 kg, g = 10 ms-2
(a) Potential energy UB at B is given by
UB = m x g x h
Substituting the values we get,
Hence, the potential energy of the pendulum at the position B = 10 J
(b) Total mechanical energy at point C = 10 J
The total mechanical energy is same at all points of the path due to conservation of mechanical energy.
(c) At A, bob has only kinetic energy which is equal to potential energy at B,
Therefore,
Exercise 2C Short Questions
5 questionsAnswer:
Whenever there is an interchange between the potential energy and kinetic energy, the total mechanical energy remains constant. This is principle of conservation of mechanical energy.
i.e K + U = constant provided there are no frictional forces.
The condition for mechanical energy to be conserved is that there should be no frictional forces. This condition is only applicable in vacuum.
Answer:
(i) For position A,
Pendulum has the maximum kinetic energy and potential energy is zero at its resting position.
So, K = mgh and U = 0
(ii) For position B,
The kinetic energy starts decreasing and the potential energy starts increasing.
So, K = 0 and U = mgh
(iii) At position C,
Kinetic energy K = 0 and potential energy U = mgh.
Answer:
(a) When the bob is at extreme position the energy possessed is potential energy.
(b) When the bob is at mean position the energy possessed is kinetic energy.
(c) When the bob is in between mean position and extreme position the energy possessed by the bob are both kinetic energy and potential energy.
Exercise 2C Very Short Questions
2 questionsAnswer:
When a body is thrown vertically upwards, its kinetic energy changes into potential energy and its velocity becomes zero.
Answer:
(a) The energy possessed at the point from where it falls is potential energy.
(b) Potential energy and kinetic energy, both are possessed at the time of fall.
(c) The energy possessed by the body on reaching the ground is kinetic.