# Energy

## Objective Questions

#### Question 1

Write true or false for each statement:

(a) A coolie does no work against the force of gravity while carrying a luggage on a plane road.

(b) The energy stored in water of a dam is kinetic energy.

(c) The energy of a flying kite is kinetic energy.

(d) Work done by a boy depends on the time in which he does work.

(e) Power spent by a body depends on the time for which it does work.

(a) True

(b) False
Correct Statement — The energy stored in water of a dam is potential energy.

(c) True

(d) False
Correct Statement — Work done by a boy depends on the magnitude of force applied and distance moved by the body in the direction of force.

(e) True

#### Question 2

Fill in the blanks:

(a) Work is said to be done by a force only when ............... .

(b) Work done = Force x ............... .

(c) The energy of a body is its capacity to do ............... .

(d) The S.I. unit of energy is ............... .

(e) The potential energy of a body is due to its ............... and kinetic energy of a body is due to its ............... .

(f) Gravitational potential energy U = mass x force of gravity on unit mass x ............... .

(g) Kinetic energy = $\dfrac{\text{1}}{\text{2}}$ x mass x ............... .

(h) Power P = ............... / time taken.

(i) The S.I. unit of power is ............... .

(j) 1 H.P. = ............... W.

(a) the body moves

(b) distance moved in the direction of force

(c) work

(d) joule

(e) state of rest or position, state of motion

(f) vertical height

(g) (speed)2

(h) Work done by the body

(i) watt (W)

(j) 746

#### Question 3

Match the following:

Column AColumn B
(a) A stone at a height(i) power
(b) A moving ball(ii) joule
(c) Energy(iii) work done in 1 sec
(d) Power(iv) potential energy
(e) watt(v) kinetic energy

Column AColumn B
(a) A stone at a height(iv) Potential energy
(b) A moving ball(v) Kinetic energy
(c) Energy(ii) joule
(d) Power(iii) work done in 1 sec
(e) watt(i) power

#### Question 4a

Select the correct alternative:

The S.I. unit of work is:

1. second
2. metre
3. joule
4. newton

joule

Reason — S.I. unit of work = S.I. unit of force x S.I. unit of distance = newton(N) x metre(m) or joule(J).

#### Question 4b

Select the correct alternative:

No work is done by a force if the body:

1. moves in the direction of force
2. does not move
3. moves in opposite direction
4. none of these

does not move

Reason — Work is said to be done if the force applied on the body makes the body move but if there is no motion in the body then work done is zero.

#### Question 4c

Select the correct alternative:

Two coolies A and B do some work in time 1 minute and 2 minute respectively. The power spent is:

1. same by both coolies
2. is more by coolie A than by B
3. is less by coolie A than by B
4. nothing can be said

is more by coolie A than by B

Reason — Power spent = $\dfrac{\text{Work done}}{\text{time taken}}$.
Since coolie A takes less time than coolie B so power spent by coolie A is more than coolie B.

#### Question 4d

Select the correct alternative:

The expression of power P is:

1. P = mgh
2. P = $\dfrac{\text{1}}{\text{2}}$ mv2
3. P = F x d
4. P = F x $\dfrac{\text{d}}{\text{t}}$

P = F x $\dfrac{\text{d}}{\text{t}}$

Reason — Power = $\dfrac{\text{Work done}}{\text{time taken}}$ and Work done = F x d
So P = F x $\dfrac{\text{d}}{\text{t}}$.

#### Question 4e

Select the correct alternative:

1 H.P. is equal to:

1. 1 W
2. 1 J
3. 764 J
4. 746 W

746 W

Reason — 1 H.P. = 746 W.

#### Question 4f

Select the correct alternative:

When a boy doubles his speed, his kinetic energy becomes:

1. half
2. double
3. four times
4. no change

four times

Reason — Kinetic energy = $\dfrac{\text{1}}{\text{2}}$ mv2
If speed gets doubled then kinetic energy becomes four times.

#### Question 4g

Select the correct alternative:

A boy lifts a luggage from height 2 m to 4 m. The potential energy will become:

1. half
2. double
3. one-third
4. one-fourth

double

Reason — Potential energy (P.E.) is given by expression mgh.
In first case P.E. = mg2 or 2mg [h=2 m]
In second case P.E. = mg4 or 4mg [h=4 m]
So potential energy gets doubled.

#### Question 1

Define work.

The work done by a force on a body is equal to the product of the force applied and the distance moved by the body in the direction of force i.e.,

Work done = Force x distance moved in the direction of force

#### Question 2

When does a force perform work?

A force performs work when it changes the position of the body or it changes the size or shape of the body.

#### Question 3

State two conditions when no work is done by a force.

The two conditions where no work is done by a force are:

1. If the force applied on a body does not move the body i.e. displacement is zero.
2. If the displacement produced by applied force is normal to the direction of force.

#### Question 4

In which of the following cases is work being done:

(a) A boy pushing a heavy rock

(b) A boy climbing up the stairs

(c) A coolie standing with a box on his head

(d) A girl moving on the road.

Work is done in the following two cases:

(b) A boy climbing up the stairs: Work is done by the boy as the boy changes his position.

(d) A girl moving on the road: Work is done as displacement is produced by the body.

#### Question 5

A coolie is moving on a road with a luggage on his head. Does he perform work against the force of gravity? Give reason for your answer.

A coolie with a luggage on his head and moving on a road does no work against force of gravity as the direction of motion of the coolie is perpendicular to the direction of force of gravity.

#### Question 6

The moon is revolving around the earth in a circular path. How much work is done by the moon?

Work done by the moon is zero as the force of attraction on moon by earth is normal to the direction of motion of moon.

#### Question 7

Write the expression for work done by a force.

Work done = Force x distance moved in the direction of force
W = F x d

#### Question 8

State the S.I. unit of work and define it.

The S.I. unit of work is joule (J). One joule of work is said to be done if one newton force when acting on a body moves it by 1 metre in the direction of force.

#### Question 9

State two factors on which the work done on a body depends.

The two factors on which the work done on a body depends are:

1. The magnitude of the force applied.
2. The distance moved by the body in the direction of force.

#### Question 10

Define the term energy.

The energy of a body is its capacity to do work. The energy of a body in a state is equal to the work done on the body to bring it to that state.

#### Question 11

State the S.I. unit of energy.

The S.I. unit of energy is joule(J).

#### Question 12

Define 1 joule of energy.

A body is said to possess an energy of 1 joule if it can do one joule work or if one joule work is done on it.

#### Question 13

How is work related to energy?

There is a direct relationship between work and energy. To do more amount of work we need to spend more energy. Similarly, the work done on a body in changing its state is said to be the energy possessed by the body.

#### Question 14

What are the two kinds of mechanical energy?

The two kinds of mechanical energy are:

1. Potential energy
2. Kinetic energy

#### Question 15

What is potential energy? State its unit.

Potential energy of a body is the energy possessed by it due to its state of rest or position. Its unit is joule (J).

#### Question 16

Give one example of a body that has potential energy, in each of the following:

(a) due to its position at a height,

(b) due to its elongated stretched state.

(a) A stone placed at a height has potential energy because of its position. It is known as gravitational potential energy.

(b) A stretched rubber band has potential energy due to its elongated stretched state. It is known as elastic potential energy.

#### Question 17

State two factors on which the potential energy of a body at a certain height above the ground depends.

The potential energy of a body at a certain height above the ground depends on the following factors:

1. The mass of the body — Greater the mass of the body, greater is the potential energy of the body.
2. Its height above the ground — More the height of the body above the ground, more is the potential energy.

#### Question 18

Two bodies A and B of masses 10 kg and 20 kg respectively are at the same height above the ground. Which of the two has greater potential energy?

Body B has greater potential energy.

Reason — Both bodies, A and B are at the same height above the ground. Value of g is also same for both. As the mass of body B (20 kg) is greater than that of body A (10 kg) hence potential energy of body B is greater.

#### Question 19

A bucket full of water is on the first floor of your house and another identical bucket with same quantity of water is kept on the second floor. Which of the two has greater potential energy?

The bucket kept on second floor has greater potential energy.

Reason — The two buckets are identical containing the same amount of water so their mass is same. Value of g is also same for the two buckets. As the bucket on second floor is at a greater height hence its potential energy is also greater.

#### Question 20

Write the expression for the gravitational potential energy explaining the meaning of the symbols used?

Gravitational potential energy (U) = mgh

where,
m is mass of the body,
g is acceleration due to gravity and
h is height of the body above ground level.

#### Question 21

A body of mass m is moved from ground to a height h. If force of gravity on mass of 1 kg is g newton, find:

(a) the force needed to lift the body,

(b) the work done in lifting the body and

(c) the potential energy stored in the body.

(a) When a body of mass m is raised to height h above ground, a force is applied.

Force needed to lift the body (F) = weight of the body

If g is the force of gravity on mass of 1 kg, then the force of gravity on mass m kg will be mg N.

F = mg N

(b) Force = mg N; distance moved = h
Work done = force x distance moved = mg x h = mgh joule

(c) The work done against the force of gravity in lifting the body to a height h is stored in the body in form of its gravitational potential energy.

Potential energy (U) = mgh joule

#### Question 22

Define the term kinetic energy. Give one example of a body which possess kinetic energy.

Kinetic energy of a body is the energy possessed by it due to its state of motion. Example: A fast moving stone has kinetic energy which has the capacity of breaking a window pane.

#### Question 23

State two factors on which the kinetic energy of a moving body depends.

The two factors on which the kinetic energy of a moving body depends are:

1. The mass of the body — Greater the mass of the body, higher is its kinetic energy.

2. The speed of the body — More the speed of the body, higher is its kinetic energy.

#### Question 24

Two toy cars A and B of masses 200 g and 500 g respectively are moving with the same speed. Which of the two has greater kinetic energy?

The toy car B has greater kinetic energy than toy car A.

Reason — The two toy cars A and B are moving with the same speed. As the toy car B has greater mass (500 g) than toy car A (200 g) hence its kinetic energy is also greater.

#### Question 25

A cyclist doubles his speed. How will his kinetic energy change: increase, decrease or remain the same?

Kinetic energy of cyclist will increase as speed is doubled because more the speed of the body, more is its kinetic energy.

#### Question 26

Write the expression for the kinetic energy of a body explaining the meaning of the symbols used.

The expression for the kinetic energy of a body (K.E.) = $\dfrac{\text{1}}{\text{2}}$ mv2
Where, m is mass of the body and
v is speed of the body.

#### Question 27

A ball of mass m is moving with a speed v. What is its kinetic energy?

Kinetic energy of ball (K.E.) = $\dfrac{\text{1}}{\text{2}}$ mv2
Where, m is mass of the ball and
v is speed of the ball.

#### Question 28

Name the form of energy stored in a wound up spring of a watch.

Potential Energy.

#### Question 29

Can a body possess energy even when it is not in motion? Explain your answer with an example.

Yes, a body can possess energy even when it is not in motion.

Example — A stone at rest placed at a height above the ground has potential energy. Water stored in a dam has potential energy.

#### Question 30

Name the type of energy (kinetic or potential) possessed by the following:

(a) A moving cricket ball.

(b) A stone at rest on the top of a building.

(c) A compressed spring.

(d) A moving bus.

(e) A bullet fired from a gun.

(f) Water flowing in a river.

(g) A stretched rubber band.

(a) A moving cricket ball has kinetic energy due to its state of motion.

(b) A stone at rest on the top of a building has potential energy due to its raised position.

(c) A compressed spring has potential energy due to its compressed state.

(d) A moving bus has kinetic energy due to its state of motion.

(e) A bullet fired from a gun has kinetic energy due to its state of motion.

(f) Water flowing in a river has kinetic energy due to its state of motion.

(g) A stretched rubber band has potential energy because of its stretched position.

#### Question 31

Give an example to show the conversion of potential energy to kinetic energy when put in use.

Consider a ball placed at a height. It will have only potential energy and no kinetic energy.

If the ball is released from the height, it falls down and the vertical height of the ball from the ground decreases. Therefore, the potential energy decreases and it changes to kinetic energy due to which the speed of the ball increases. During the fall, the ball has both the potential energy and the kinetic energy. As the ball reaches the ground, the potential energy becomes zero and it changes entirely into kinetic energy.

The below figure shows the conversion of potential energy into kinetic energy during the vertical free fall of a ball at various positions A, B and C.

#### Question 32

State the energy changes that occur in a watch spring while it unwinds.

In a wound up watch spring the energy stored is potential energy. When the watch spring unwinds itself, the potential energy changes into kinetic energy and this kinetic energy is used to move the arms of the watch.

#### Question 33(a)

Give reasons for the following:

No work is done if a man is pushing against a wall.

Work is said to be done only when there is change in position or size and shape of the body. When a man pushes the wall it does not move so no work is done.

#### Question 33(b)

Give reasons for the following:

Hammer drives a nail into the wood only when it is lifted up and then struck.

When a hammer is lifted it has potential energy due to its raised position and then when it is struck it drives the nail into the wood due to its potential energy.

#### Question 33(c)

Give reasons for the following:

A horse and a dog are running with the same speed. Which one of them has more kinetic energy than the other?

A horse has more kinetic energy than a dog. Kinetic energy of a body depends on mass and speed of the body. Since both dog and horse have same speed but mass of horse is more than that of dog so horse has more kinetic energy than a dog.

#### Question 33(d)

Give reasons for the following:

A teacher moving around in the class is doing work but a child standing and reading a book is not doing any work.

As the teacher moves around in the class, he/she is in a state of motion, there is change in his/her position due to application of force. Hence, work is done by the teacher.
On the other hand, a child standing and reading a book is stationary. There is no change in his/her position. Hence, no work is done by the child.

#### Question 34

State the energy changes in the following while in use:

(a) An electric bulb

(b) An electric oven

(c) A loudspeaker

(d) A microphone

(e) An electric motor

(a) When an electric bulb glows, the electrical energy changes into heat and light energy.

(b) In electric oven, electrical energy changes into heat energy.

(c) In loudspeaker, electrical energy is converted into sound energy.

(d) A microphone converts sound energy into electrical energy.

(e) An electric motor converts electrical energy into mechanical energy.

## Numericals

#### Question 1

A force of 30 N acts on a body and moves it through a distance of 5 m in the direction of force. Calculate the work done by the force.

Given:
Force (F) = 30 N
Distance (d) = 5 m
Work done (W) = ?

Work done = Force x distance = 30 N x 5 m = 150 J

So, the work done by the force = 150 J.

#### Question 2

A man lifts a mass of 20 kg to a height of 2.5 m. Assuming that the force of gravity on 1 kg mass is 10 N, find the work done by the man.

Given:
Mass (m) = 20 kg
Distance (d) = Height = 2.5 m
Force of gravity on mass of 1 kg = 10 N
Work done (W) = ?

Force (F) = mg = 20 x 10 = 200 N

Work done = Force x distance = 200 x 2.5 = 500 J

So, the work done by the man = 500 J.

#### Question 3

A body when acted upon by a force of 10 kgf moves to a distance 0.5 m in the direction of force. Find the work done by the force. Take 1 kgf = 10 N.

Given:
1 kgf = 10 N
10 kgf = 10 x 10 = 100 N
So, Force (F) = 100 N
Distance (d) = 0.5 m
Work done (W) = ?

Work done = Force x distance = 100 x 0.5 = 50 J

So, the work done by the force = 50 J.

#### Question 4

Two bodies of same masses are placed at height h and 2h. Compare their gravitational potential energy.

Given:
Mass of first body = Mass of second body = m
Height of first body = h
Height of second body = 2h
g is same for both the bodies.

We know Gravitational potential energy = mgh

Gravitation potential energy of first body (U1) = mgh
Gravitation potential energy of second body (U2)= mg2h

On comparing both gravitational potential energy:

$\dfrac{\text{U}_1}{\text{U}_2} = \dfrac{\text{mgh}}{\text{mg2h}} = \dfrac{\text{1}}{\text{2}}$

So, gravitational potential energy of first body : gravitational potential energy of second body = 1:2.

#### Question 5

Find the gravitational potential energy of 2.5 kg mass kept at a height of 15 m above the ground. The force of gravity on mass 1 kg is 10 N.

Given:
Mass (m) = 2.5 kg
Height (h) = 15 m
Force of gravity on mass 1 kg = 10 N

Gravitational potential energy (U) = mgh = 2.5 x 10 x 15 = 375 J

So, gravitational potential energy = 375 J.

#### Question 6

The gravitational potential energy stored in a box of weight 150 kgf is 1.5 x 104 J. Find the height of the box. Take 1 kgf = 10 N.

Given:
Gravitational potential energy (U) = 1.5 x 104 J = 15000 J
Weight = 150 kgf = 150 x 10 = 1500 N
height h = ?

U = mgh

15000 = 1500 x h

h = $\dfrac{\text{15000}}{\text{1500}}$

h = 10 m

So height of the box = 10 m.

#### Question 7

The potential energy of a body of mass 0.5 kg increases by 100 J when it is taken to the top of a tower from the ground. If the force of gravity on 1 kg = 10 N, what is the height of the tower?

Given:
Potential energy (U) = 100 J
Mass (m) = 0.5 kg
Force of gravity on 1 kg mass = 10 N
height (h) = ?

U = mgh

100 = 0.5 x 10 x h

h = $\dfrac{\text{100}}{\text{5}}$

h = 20 m

So height of the tower = 20 m.

#### Question 8

A body of mass 60 kg is moving with a speed 50 m s-1. Find its kinetic energy.

Given:
Mass (m) = 60 kg
Speed (v) = 50 m s-1
Kinetic energy = ?

Kinetic energy = $\dfrac{\text{1}}{\text{2}}$ x mv2

= $\dfrac{\text{1}}{\text{2}}$ x 60 x (50)2

= 30 x 2500

= 75000 J or 7.5 x 104 J

So kinetic energy = 7.5 x 104 J.

#### Question 9

A truck of mass 1000 kg increases its speed from 36 km h-1 to 72 km h-1. Find the increase in its kinetic energy.

Given:

Mass (m) = 1000 kg

1 km h-1 = $\dfrac{\text{5}}{\text{18}}$ m s-1

36 km h-1 = $\dfrac{\text{5}}{\text{18}}$ x 36 = 10 m s-1

So, initial speed (v1) = 10 m s-1

1 km h-1 = $\dfrac{\text{5}}{\text{18}}$ m s-1

72 km h-1 = $\dfrac{\text{5}}{\text{18}}$ x 72 = 20 m s-1

So, final speed (v2) = 72 km h-1 = 20 m s-1

Increase in its kinetic energy = ?

Increase in kinetic energy = $\dfrac{\text{1}}{\text{2}}$ m[(v2)2 - (v1)2]

= $\dfrac{\text{1}}{\text{2}}$ x 1000 x [(20)2 - (10)2]

= 500 x [400 - 100]

= 500 x 300

= 150000 J or 1.5 x 105 J

So increase in kinetic energy = 1.5 x 105 J.

#### Question 10

A car is moving with a speed of 15 km h-1 and another identical car is moving with a speed of 30 km h-1. Compare their kinetic energy.

Speed of first car = 15 km h-1
Speed of second car = 30 km h-1
Mass of both cars = m

Kinetic energy of first car (K1) = $\dfrac{\text{1}}{\text{2}}$ x mv2

= $\dfrac{\text{1}}{\text{2}}$ x m x (15)2

= $\dfrac{\text{225}}{\text{2}}$ x m

= 112.5 m J

Kinetic energy of second car (K2) = $\dfrac{\text{1}}{\text{2}}$ x mv2

= $\dfrac{\text{1}}{\text{2}}$ x m x (30)2

= $\dfrac{\text{900}}{\text{2}}$ x m

= 450 m J

Comparing the kinetic energy we get:

$\dfrac{\text{K}_1}{\text{K}_2} = \dfrac{\text{112.5 m}}{\text{450 m}} = \dfrac{\text{1}}{\text{4}}$

So Kinetic energy of first car (K1) : Kinetic energy of second car (K2) = 1 : 4.

#### Question 11

A pump raises water by spending 4 x 105 J of energy in 10 s. Find the power of pump.

Given:
Work done by pump = Energy spent = 4 x 105 J or 400000 J
time = 10 s
Power = ?

Power = $\dfrac{\text{Work done}}{\text{time taken}}$

= $\dfrac{\text{400000}}{\text{10}}$

= 40000 W or 4 x 104 W

So power spent by the pump = 4 x 104 W.

#### Question 12

It takes 20 s for a girl A to climb up the stairs while girl B takes 15 s for the same job. Compare:

(a) The work done and

(b) The power spent by them.

(a) Both the girls move the same distance and force is also equal on both. Hence, the work done by both the girls is the same.
∴ Work done by girl A : Work done by girl B = 1 : 1

(b) Power spent = $\dfrac{\text{Work done}}{\text{time taken}}$

We know,

Work done by girl A = Work done by girl B = W

Power spent by girl A (PA) = $\dfrac{\text{W}}{\text{20}}$

Power spent by girl B (PB) = $\dfrac{\text{W}}{\text{15}}$

Comparing the power spent by girl A and girl B:

$\dfrac{\text{P}_\text{A}}{\text{P}_\text{B}} = \dfrac{\dfrac{\text{W}}{\text{20}}}{\dfrac{\text{W}}{\text{15}}} \\[1em] = \dfrac{\text{15}}{\text{20}} = \dfrac{\text{3}}{\text{4}}$

∴ Power spent by girl A : Power spent by girl B = 3:4.