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
Soln:
Answer is (c) remains constant
Explanation
Body falling freely towards the earth possess the same kinetic and potential energy
and it follows the Law of conservation of energy hence its total energy remains
constant.
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
Soln:
Answer is (a) does not change
Explanation:
Potential energy is the product of height, mass and gravity. Hence height is a factor
in determining potential energy. Here the height does not change hence potential
energy of the car does not change.
3. In case of negative work the angle between the force and displacement is
(a) 00
(b) 450
(c) 900
(d ) 1800
Soln:
Answer is (d) 1800
Explanation:
work done = FS cosɵ
Cos180 = -1
Hence the answer is 1800
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
Soln:
(a) acceleration
Explanation:
Momentum, potential energy and kinetic energy varies with weight. But in this case,
acceleration is because of acceleration due to gravity which is independent of mass
hence acceleration is the right answer.
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 gravitational force will be (g =10
m s–2)
(a) 6 ×103 J
(b) 6 J
(c) 0.6 J
(d) zero
Soln:
(d) zero
Explanation:
Here Direction of work done is perpendicular to gravitational force direction. Hence
the work done against the gravity is zero.
6. Which one of the following is not the unit of energy?
(a) joule
(b) newton metre
(c) kilowatt
(d) kilowatt-hour
Soln:
Answer is (c) kilowatt
Explanation:
Kilowatt is the SI Unit of electrical power
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
Soln:
Answer is (d) initial velocity of the object
Explanation:
Work done is the product of force and displacement hence force and displacement
are the required attributes for the work to be done. But work done is not dependent
on initial velocity.
8. Water stored in a dam possesses
(a) no energy
(b) electrical energy
(c) kinetic energy
(d) potential energy
Soln:
Answer is (d) potential energy
Explanation:
Potential energy is the energy stored in an object because of the position. Water in
the dam possesses energy because of position hence it is potential energy.
9. A body is falling from a height h. After it has fallen from a height h2, 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
Soln:
Answer is (c) half potential and half kinetic energy
Explanation:
When body is at height h, its potential will be hundred per cent and kinetic energy will
be zero. In the same way, when the body reaches the ground its potential energy will
be zero and kinetic energy will be maximum. At height h/2 both potential energy and
kinetic energy of the body will be half.
Short-answer Questions
10. A rocket is moving up with a velocity v. If the velocity of this rocket is
suddenly tripled, what will be the ratio of two kinetic energies?
Soln:
Initial velocity = v = 3v
Initial kinetic energy =
12
v2
Kinetic energy =
12
v2
12
m(3v)2 = 9(
12
mv2)
Ratio between Initial kinetic energy and final kinetic energy is 1:9
11. Avinash can run with a speed of 8 m s–1 against the frictional force of 10 N,
and Kapil can move with a speed of 3 m s–1 against the frictional force of 25 N.
Who is more powerful and why?
Soln:
P= f×v
P1= 10× 8 = 80W
P2=25×3=75W
Hence Avinash is more powerful than Kapil
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.
Soln:
Total distance travelled by the boy = 1500 m + 200 m + (1.5 x 2 πr)
Total distance travelled by the boy = 1500 m + 200 m + (1.5 x 2 x 3.14 x 100)= 4442
m
Frictional force = 5 N
Workdone = force × Displacement
Workdone = 5 ×4442 = 22210 J
13. Can any object have mechanical energy even if its momentum is zero?
Explain.
Soln:
Momentum is the product of mass and velocity. If the body is at rest its velocity will
be zero. If it is rest at the height it possesses gravitational potential energy hence
mechanical energy.
14. Can any object have momentum even if its mechanical energy is zero?
Explain.
Soln:
No, Because its potential and kinetic energy are zero.
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 s–2)
Soln:
Power of pump = 2kW =2000W
Time (t)= 60sec
Height (h) = 10m g = 10m/s2
Power =work done per unit time.
Work done = mgh = m ×10×10 =100m
= 2000W
Therefore, m = 1200 kg So, the pump can raise 1200kg of water in one minute.
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?
Soln:
Person on planet A can jump a height of 0.8 m because the weight of the person on
plat A is half the weight that of earth. Hence acceleration due to gravity on planet A
will also be half of that on earth.
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.
Soln:
v2-u2 = 2as
s= v2-u2/2a
F = ma
W = ma(v2-u2)/2a
12
mv2 -
12
mu2
=(K.E)f-(K.E)t
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.
Soln:
Force always acts in perpendicular to the displacement direction. If the object is
moving in circular path then no work will be done despite of action of a force.
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 s–2).
Soln:
mgh=m×10×10= 100m joules
when 40% energy is reduced remaining energy will be 60mjoules
Hence 60 – m x 10 × h
H = -6m
20. If an electric iron of 1200 W is used for 30 minutes everyday, find electric
energy consumed in the month of April.
Soln:
Power of electric iron=1200W
Usage per day = 30min
=30/60hrs
=0.5hrs
Number of days in the month of April=30days
Electrical energy consumed, E=Pxt 1200×0.5×30
=18000WH
=18KWH
=18units
Therefore, The Total Electricity consumed in April month 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?
Soln:
Kinetic energy equation: Ek=1/2 mv2
Momentum equation: p=mv
Kinetic energy equation in terms of momentum: Ek = p2/2m
Kinetic energy of two objects will be the same if their mass and momentum are the
same. Among light and heavy bodies, Heavy body has highest momentum. When
the momentum is the equal light body has more kinetic energy.
22. An automobile engine propels a 1000 kg car (A) along a levelled road at a
speed of 36 km h–1. 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.
Soln:
m(A)= m(B) = 1000 kg.
v = 36 km/h =10 m/s
Frictional force = 100 N
car A moves with a uniform speed, which means engine of car applies a force equal
to the frictional force
Power = Force × distance / time = F . V
= 100 N × 10 m/s = 1000 W
After collision mA uA + mB uB = mA vA + mB vB.
1000 × 10 + 1000 × 0
= 1000 × 0 + 1000 × vB vB
= 10 m s–1
23. A girl having a mass of 35 kg sits on a trolley of mass 5 kg. The trolley is
given an initial velocity of 4 m s–1 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?
Soln:
Initial velocity of the trolley,u = 4 m/s
Final velocity of the trolley v = 0
Mass of the trolley m = 5 kg
Distance covered by the trolley before coming to rest,s = 16 m
From Equation 2 as = v2-u2,
a = v2-u22 S
= 0-(4)22×16
= 0.5 m/s2
Force (frictional) acting on the trolley = ma
= 40 (- 0.5)
= – 20 N
Work done on the trolley = Fs = (20 N) (16 m)
= 320 J
(b) Since the girl does not move w.r.t. the trolley (as she is sitting on it), work done
by the girl = 0.
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 s –2)
Soln:
(a)
F= 250kg x g = 2500 N
S= 1m
W=F.s= 250Nm = 2500 J
(b)
While holding box there is no displacement hence work done is zero
c) While holding the box they apply a muscular force which is equal and opposite to
the gravitational force hence they feel tired while holding box.
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 waterfalls
from it in a minute. Calculate the equivalent power if all this energy can be
utilized? (g = 10 m s–2)
Soln:
Power is the rate of transfer of energy or the rate of doing work. Watt is the unit of
power and kilowatt is 1000 watts.
h = 20 m, and mass = 2000 × 103 kg
= 2 × 106 kg
Power = m g h / t
= 2 x 106 x 10 x 20 / 60
w = 4/6 x 107
w = 2/3 x 107w
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 a
constant speed of 1 m s –1 vertically? (g = 10 m s–2)
Soln:
Power = work/time
work = force x displacement
force = mass x acceleration
acceleration = velocity/time
Therefore
Power = velocity × mass × displacement / time × time
Here
Power,P=100W
velocity,v=1m/s
since time,t=1s
displacement, s=1m
acceleration,a=10m/s
From equation P=m×a×s / t
100=m×10
m=10
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–1?
Soln:
Power of an object which does work at 1 Joule/sec is called watt.
1 watt =
joulesecond
1 kilowatt = 1000watts = 1000J/sec
mass of car = 150kg
power for each kg = 500x 150=7500w
speed = 20m/s
power = Force x v
∴force=power/v = 7500/20
=350N
28. Compare the power at which each of the following is moving upwards
against the force of gravity? (given g = 10 m s–2) (i) a butterfly of mass 1.0 g
that flies upward at a rate of 0.5 m s–1. (ii) a 250 g squirrel climbing up on a
tree at a rate of 0.5 m s–1.
Soln:
1. Butterfly force= mg=1/100power=f×s÷t. {s÷t=velocity}power=1÷100×.5power=1÷200W
2. squirrel force=mg=25power=25×.5power=12.5W
