Work Power Energy

EXERCISE # 1
Part - I
SECTION (A) : WORK DONE BY CONSTANT FORCE
A 1. A block of mass m is pulled on a rough horizontal surface which has a friction coefficient  A horizontal force F is
applied which is capable of moving the body uniformly with speed v. Find the work done on the block in time t by (a)
weight of the block, (b) Normal reaction by surface on the block, (c) friction, (d) F.

A 2. A gardener pulls a lawn roller along the ground through a distance of 20 m. If he applies a force of 20 kg wt in a direction
inclined at 60º to the ground, find the work done by him. (Take g = 10 m/s2)

A 3. Calculate the work done against gravity by a coolie in carrying a load of mass 10 kg on his head when he moves
uniformly a distance of 5 m in the (i) horizontal direction (ii) upwards vertical direction.
(Take g = 10 m/s2)

A 4. A body is constrained to move in the y-direction. It is subjected to a force (–2 î + 15 ĵ + 6 k̂ ) Newton. What is the work
done by this force in moving the body through a distance of 10 m in positive y direction ?

A 5. Figure shows a particle sliding on a frictionless track which terminates in a

straight horizontal section. If the particle starts slipping from the point A, how A

far away from the track will the 1.0m

0.5m
particle hit the ground ?

A 6. A block of mass 500 g slides down on a rough incline plane of inclination 53° with a uniform speed. Find the work done
against the friction as the block slides through 2 m. [g = 10 m/s2]

A 7. A block of mass 20 kg is slowly slid up on a smooth incline of inclination 53° by a person. Calculate the work done by
the person in moving the block through a distance of 4 m, if the driving force is (a) parallel to the incline and (b) in the
horizontal direction. [g = 10 m/s2]

SECTION (B) : WORK DONE BY A VARIABLE FORCE

B 1. A particle moves along the x-axis from x = 0 to x = 5 m under the influence of a force F(in N) given by
F = 3x2 – 2x + 7. Calculate the work done by this force.
B 2. Adjacent figure shows the force-displacement graph of a moving body, what is the work done by this force in displacing
body from x = 0 to x = 35 m ?

20–
a (cm/sec )

B 3. A 10 kg mass moves along x-axis. Its acceleration as function of its

2

15–
position is shown in the figure. What is the total work done on the 10–
mass by the force as the mass 5–
moves from x = 0 to x = 8 cm ?
0 2 4 6 8 x(cm)

B 4. A chain of length  and mass m is slowly pulled at constant speed up over the edge of a table by a force parallel to the
surface of the table. Assuming that there is no friction between the table and chain, calculate the work done by force till
the chain reaches to the horizontal surface of the table.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 93
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
SECTION (C) : WORK ENERGY THEOREM
C 1. A bullet of mass 20 g is found to pass two points 30 m apart in a time interval of 4 second. Calculate the kinetic energy
of the bullet if it moves with constant speed.

C 2. In a ballistics demonstration, a police officer fires a bullet of mass 50.0 g with speed 200 m s–1 on soft plywood of
thickness 2.00 cm. The bullet emerges with only 10% of its initial kinetic energy. What is the emergent speed of the
bullet ?

C 3. It is well known that a raindrop or a small pebble falls under the influence of the downward gravitational force and the
opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined.
Consider a drop or small pebble of 1 g falling (from rest) from a cliff of height 1.00 km. It hits the ground with a speed of
50.0 m s–1. What is the work done by the unknown resistive force?

C 4. A bullet of mass 20 g is fired from a rifle with a velocity of 800 ms–1. After passing through a mud wall 100 cm thick,
velocity drops to 100 m s-1. What is the average resistance of the wall ? (Neglect friction due to air and work of gravity)

C 5. A force of 1000 N acts on a particle parallel to its direction of motion which is horizontal. Its velocity increases from 1
m s–1 to 10 m s–1, when the force acts through a distance of 4 metre. Calculate the mass of the particle. Given : a force
of 10 Newton is necessary for overcoming friction.

C 6. A rigid body of mass 5 kg initially at rest is moved by a horizontal force of 20 N on a frictionless table. Calculate the work
done by the force on the body in 10 second and prove that this equals the change in kinetic energy of the body.

C 7. A rigid body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with
coefficient of kinetic friction = 0.1. Calculate the
(a) work done by the applied force on the body in 10 s. (b) work done by friction on the body in 10 s.
(c) work done by the net force on the body in 10 s. (d) change in kinetic energy of the body in 10 s.

C 8. A body of mass 5 kg is acted upon by a variable force. The force varies with the
distance covered by the body. What is the speed of the body when the
body has covered 25 m? Assume that the body starts from rest.

C 9. A block of mass m moving at a speed v compresses a spring through a distance x before its speed becomes one fourth.
Find the spring constant of the spring.

C-10. Consider the situation shown in figure. Initially the spring is undeformed when the system is released from rest.
Assuming no friction in the pulley, find the maximum elongation of the spring.

C-11. A rigid body of mass 0.3 kg is taken slowly up an inclined plane of length 10 m and height 5 m, and then allowed to slide
down to the bottom again. The co-efficient of µ = 0.15

0.3
kg

Fixed

friction between the body and the plane is 0.15.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 94
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
Using g = 9.8 m/s2 find the
(a) work done by the gravitational force over the round trip.
(b) work done by the applied force(assuming it to be parallel to the inclined plane) over the upward journey
(c) work done by frictional force over the round trip.
(d) kinetic energy of the body at the end of the trip?

C 12. As shown in figure, there is pulley block system. The system is released
from rest and the block of mass 2kg is found to have a speed 0.3 m/s after it
has descended through a distance of 2m. Find the coefficient of kinetic friction
between the block and the
table. (g = 10 m/s2)

C-13. A block of mass 200 g is moving with a speed of 4 m/s at the highest point in a closed circular tube of radius 10 cm kept
in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations
inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.
(g = 10 m/s2)

C-14. A block of mass m sits at rest on a frictionless table in a train that is moving
with speed vc along a straight horizontal track (fig.) A person in the train
pushes on the block with a net horizontal force
F for a time t in the direction of the car’s motion.
(i) What is the final speed of the block according to a person in the train?
(ii) What is the final speed of the block according to a person standing on the ground outside the train?
(iii) How much did kinetic energy of the block change according to the person in the car?
(iv) How much did kinetic energy of the block change according to the person on the ground?
(v) In terms of F, m & t how far did the force displace the object according to the person in car?
(vi) According to the person on the ground?
(vii) How much work does each say the force did?
(viii) Compare the work done to the K gain according to each person.
(ix) What can you conclude from this computation?

SECTION (D) : POTENTIAL ENERGY AND MECHANICAL ENERGY CONSERVATION

D 1. A projectile is fired from the top of a 40 m high cliff with an initial speed of 50 m/s at an unknown angle. Find its speed
when it hits the ground. (g = 10 m/s2)

D 2. A rain drop of radius 2 mm falls from a height of 250 m above the ground. What is the work done by the gravitational
force on the drop? (Density of water = 1000 kg/m 3)

D 3. Calculate the velocity of the bob of a simple pendulum at its mean position if it is able to rise to a vertical height of 10
cm. Given : g = 980 cm s–2.

D 4. The bob of a pendulum is released from a horizontal position A as shown in

figure. If the length of the pendulum is 2 m, what is the speed with which the
bob arrives at the lowermost point B, given that it dissipated 10% of its initial
potential energy w.r.t. B point
///////////////////////
against air resistance? (g = 10 m/s2)

D 5. The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension
in the string is 16.0 N when the system is set into motion. Find the decrease in the gravitational
potential energy during the first second after the system m1
is released from rest. m2
Atwood Machine

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 95
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
///////////////////////
D 6. The two blocks in an Atwood machine have masses 2.0 kg and 3.0 kg. Find the work
done by gravity during the fourth second after the system is
released from rest. (g = 10 m/s2)

m1
m2
D 7. A 1 kg block situated on a rough inclined plane is connected to a spring of Atwood Machine
spring constant 100 N m–1 as shown in figure. The block is released from rest
with the spring in the unstretched position. The block moves 10 cm along the
incline before coming to rest. Find the coefficient of friction between the
block and the incline assume that the sprin3g has negligible mass and the 1 kg
pulley is
frictionless. Take g = 10 ms–2. Fixed
37º

SECTION (E) : POWER

E 1. An elevator of mass 500 kg is to be lifted up at a constant velocity of 0.4 m s–1. What should be the minimum horse
power of the motor to be used? (Take g = 10 m s–2 and 1 hp = 750 watts).

E 2. A lift is designed to carry a load of 4000 kg in 10 seconds through 10 floors of a building averaging 6 metre per floor .
Calculate the horse power of the lift. (Take g = 10 m s–2 and 1 hp = 750 watts).

E 3. A labourer lifts 100 stones to a height of 6 metre in two minute. If mass of each stone be one kilogram, calculate the
average power. Given : g = 10 m s–2.

E 4. A motor is capable of raising 400 kg of water in 5 minute from a well 120 m deep. What is the power developed by the
motor? [g = 10 m/sec2 ]

E 5. A man of mass 70 kg climbs up a vertical staircase at the rate of 1 ms–1. What is the power developed by the man? [g
= 10 m/sec2]

E 6. The power of a pump motor is 2 kilowatt. How much water per minute can it raise to a height of 10 metre? Given : g =
10 m s–2.

E 7. An engine develops 10 kW of power. How much time will it take to lift a mass of 200 kg through a height of 40 m? Given
: g = 10 ms–2.

E 8. How much minimum power of a water pump needed to lift water from a level 20 m below the ground at a rate of 20 kg
/min. (746 W = 1 hp) (g = 10 m/s2)

E 9. In a factory an engine of 5.3HP is to be used to lift 4000 kg of coal through a distance of 12 m. calculate the time taken
by engine to do this.
SECTION (F) : CONSERVATIVE & NONCONSERVATIVE FORCES AND EQUILIBRIUM
F 1. A force F = x2y2i + x2y2j (N) acts on a particle which moves in the XY plane.

(a) Determine F is conservative or not and

(b) find the work done by F as it moves the particle from A to C (fig.) along each of the paths ABC, ADC, and AC.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 96
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
F 2. Calculate the forces F(y) associated with the following one-dimensional potential energies:
(a) U = –  y (b) U = ay3 – by2 (c) U = U 0 sin y
F 3. The potential energy function of a particle in a region of space is given as :
U = (2x2 + 3y3 + 2z) J
Here x, y and z are in metres. Find the force acting on the particle at point P(1m, 2m, 3m).
F 4. Force acting on a particle in a conservative force field is :
  
(i) F  (2 î  3 ĵ ) (ii) F  (2 x î  2y ĵ) (iii) F  ( y î  xĵ)
Find the potential energy function, if it is zero at origin.

F 5. The potential energy function for a particle executing linear simple harmonic
1 2
motion is given by U(x) = kx , where k is the force constant. For k = 0.5 N
2
m –1, the graph of U(x) versus x is shown figure. Show that a particle of total
energy 1 J moving under this
potential ‘turns back’ when it reaches x = ± 2m.

Part - II
* Marked Questions are having more than one correct option.
SECTION : (A) WORK DONE BY CONSTANT FORCE
mv 2
A 1. A rigid body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is and is
r
directed towards the centre. What is the work done by this force in moving the body over half the cirumference of the
circle.

mv 2 mv 2 r 2
(A) (B) Zero (C) (D)
r 2 r2 mv 2
A 2. If the unit of force and length each be increased by four times, then the unit of work is increased by
(A) 16 times (B) 8 times (C) 2 times (D) 4 times

A 3. A man pushes wall and fails to displace it. He does

(A) Negative work (B) Positive but not maximum work
(C) No work at all (D) Maximum work

A 4. A rigid body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done by this
force on the body is 25 joules, the angle which the force makes with the direction of motion of the body is
(A) 0º (B) 30º (C) 60º (D) 90º

A 5. A rigid body of mass m kg is lifted uniformly by a man to a height of one metre in 30 sec. Another man lifts the same
mass uniformly to the same height in 60 sec. The work done on the body against gravitation by them are in ratio
(A) 1 : 2 (B) 1 : 1 (C) 2 : 1 (D) 4 : 1

A 6. The work done in slowly pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an
angle of 15º with the horizontal by a force parallel to the incline is
(A) 4.36 kJ (B) 5.17 kJ (C) 8.91 kJ (D) 9.82 kJ

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 97
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
A 7. A 50 kg man with 20 kg load on his head climbs up 20 steps of 0.25 m height each. The work done by the
man on the block during climbing is
(A) 5 J (B) 350 J (C) 1000 J (D) 3540 J
 
A 8. A particle moves from position r1  3 î  2 ĵ  6k̂ to position r2  14 î  13 ĵ  9 k̂ under the action of force

4 î  ĵ  3 k̂ N . The work done by this force will be

(A) 100 J (B) 50 J (C) 200 J (D) 75 J

A 9. A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third
second of the motion of the ball is
(A) 1 : 2 : 3 (B) 1 : 4 : 9 (C) 1 : 3 : 5 (D) 1 : 5 : 3
A 10. A block of mass m is suspended by a light thread from an elevator. The elevator is
accelerating upward with uniform acceleration a. The work done by tension
on the block during t seconds is (u = 0) :
m m m
(A) (g + a) at2 (B) (g – a)at2 (B) gat2 (D) 0
2 2 2

A 11.* If the resultant force is always perpendicular to motion of a particle

(A) KE remains constant (B) work done = 0
(C) speed is constant (D) velocity is constant

A 12.* Work done by force of friction

(A) can be zero (B) can be positive
(C) can be negative (D) information insufficient

A 13.* When work done by force of gravity is negative (Assume only gravitational force to be acting)
(A) KE increases (B) KE decreases
(C) PE increases (D) PE stays constant

A 14.* When total work done on a particle is positive

(A) KE remains constant (B) Momentum increases
(C) KE decreases (D) KE increases

A 15.* When a man walks on a horizontal surface with constant velocity, work done by
(A) friction is zero (B) contact force is zero
(C) gravity is zero (D) None of these
SECTION (B) : WORK DONE BY A VARIABLE FORCE
B 1. A particle moves under the effect of a force F = Cx from x = 0 to x = x1. The work done in the process is
1
(A) Cx12 (B) Cx 12 (C) Cx1 (D) Zero
2
B 2. Two springs have their force constant as k1 and k2(k1 > k2). When they are stretched by the same constant force up to
equilibrium -
(A) No work is done by this force in case of both the springs
(B) Equal work is done by this force in case of both the springs
(C) More work is done by this force in case of second spring
(D) More work is done by this force in case of first spring
B 3. A rigid body is acted upon by a horizontal variable force which is inversely proportional to the distance covered
from its initial position ‘s’. The work done by this force will be proportional to :
(A) s (B) s2 (C) s (D) None of these

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 98
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
B 4. The work done by the frictional force on a surface in drawing a circle of radius r on the surface by a pencil of
negligible mass with a normal pressing force N (coefficient of friction µ k) is :
(A) 4r2 K N (B) –2r2 K N (C) –2r K N (D) zero

B 5. A force acting on a particle varies with the displacement x as F = ax – bx2. Where a = 1 N/m and b = 1 N/m 2. The
work done by this force for the first one meter (F is in newtons, x is in meters) is :
1 2 3
(A) J (B) J (C) J (D) None of these
6 6 6

SECTION (C) : WORK ENERGY THEOREM

C 1. The kinetic energy of a body of mass 2 kg and momentum of 2 Ns is
(A) 1 J (B) 2J (C) 3 J (D) 4 J

C 2. A particle of mass m at rest is acted upon by a force F for a tim e t. Its kinetic energy after an
interval t is :

F2 t 2 F2 t 2 F2 t 2 Ft
(A) (B) (C) (D)
m 2m 3m 2m

C 3. The graph between the magnitude of resistive force F acting on a body and
the position of the body travelling in a straight line is shown in the figure. The
mass of the body is 25 kg and initial velocity is 2 m/s. When the distance
covered by the body is 4m,
its kinetic energy would be (not other force acts on it)
(A) 50 J (B) 40 J
(C) 20 J (D) 10 J
C 4. A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. If it starts its journey from
rest at x = 0, its velocity at x = 12 m is

(A) 0 m/s (B) 20 2 m/s (C) 20 3 m/s (D) 40 m/s

C 5. A particle is projected horizontally from a height h. Taking g to be constant every where, kinetic energy E of the particle
with respect to time t is correctly shown in (Neglect air resistance)

(A) (B) (C) (D)

C 6. If v, p and E denote the megnitude of velocity, momentum and kinetic energy of the particle, then :
(A) p = dE/dv (B) p = dE/dt (C) p = dv/dt (D) None of these
C 7. A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is
thrown
(A) vertically downward (B) vertically upward
(C) horizontally (D) the speed does not depend on the initial direction.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 99
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
C 8. A body moving at 2 m/s can be stopped over a distance x. If its kinetic energy is doubled, how long will it go
before coming to rest, if the retarding force remains unchanged ?
(A) x (B) 2x (C) 4x (D) 8x
C 9. A retarding force is applied to stop a train. The train stops after 80 m. If the speed is doubled, then the distance travelled
when same retarding force is applied is
(A) The same (B) Doubled (C) Halved (D) Four times
C 10. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any
displacement x is proportional to
(A) x2 (B) ex (C) x (D) logex

C 11. A block weighing 10 N travles down a smooth curved track AB joined to a

rough horizontal surface (figure). The rough surface has a friction coefficient
of 0.20 with the block. If the block starts slipping on the track from a point 1.0
m above the horizontal surface, the
distance it will move on the rough surface is :
(A) 5.0 m (B) 10.0 m (C) 15.0 m (D) 20.0 m
C 12. A small mass slides down an inclined plane of inclination  with the horizontal. The co-efficient of friction is
 =  0 x where x is the distance through which the mass slides down and  0 is a constant. Then the distance
covered by the mass before it stops is:
2 4 1 1
(A) tan  (B) tan  (C) tan  (D) tan 
0 0 2 0 0

C 13. A toy car of mass 5 kg starts from rest and moves up a ramp under the influence of force F (F is applied in the direction
of velocity) plotted against displacement x. The maximum height attained is given by (g = 10 m/s2)

ymax

x=0 x=11m
(A) ymax = 20 m (B) ymax = 15 m (C) ymax = 11 m (D) ymax = 5 m

SECTION (D) : MECHANICAL ENERGY CONSERVATION

D 1. The negative of the work done by the conservative internal forces on a system equals the change in its
(A) total energy (B) kinetic energy (C) potential energy (D) none of these

D 2. A body is dropped from a certain height. When it loses U amount of its energy it acquires a velocity ‘v’. The mass
of the body is :
(A) 2U/v2 (B) 2v/U2 (C) 2v/U (D) U2/2v

D 3. A stone is projected vertically up with a velocity u, reaches upto a maximum height h. When it is at a height of
3h/4 from the ground, the ratio of KE and PE at that point is : (consider PE = 0 at the point of projection)
(A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 3 : 1

D 4. A bob hangs from a rigid support by an inextensible string of length . If it is displaced through a
distance  (from the lowest position) keeping the string straight & then
released. The speed of the bob at the lowest position is :
(A) g (B) 3g  (C) 2g  (D) 5g 

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 100
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
D 5. Two springs A and B (kA = 2kB) are stretched by applying forces of equal magnitudes at the four ends. If the energy
stored in A is E, then in B is (assume equilibrium):
(A) E/2 (B) 2E (C) E (D) E/4

D 6. When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will
be increased by
(A) 100 J (B) 200 J (C) 300 J (D) 400 J

D 7. A block of mass m is attached to two unstretched springs of spring constants

k1 and k2 as shown in figure. The block is displaced towards right through a
distance x and is released. Find the speed
of the block as it passes through the mean position shown.

k1  k 2 k 1k 2 k 12k 22 k 13k 32
(A) x (B)
m m(k 1  k 2 ) x (C)
m(k 12  k 22 )
x (D)
m(k 13  k 32 )

D 8. A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is
equal to
(A) 4 J (B) 54 J (C) 415 J (D) 100 J

D 9. A spring of spring constant k placed horizontally on a rough horizontal surface is compressed against a block of
mass m placed on the surface so as to store maximum energy in the spring. If the coefficient of friction between
the block and the surface is µ, the potential energy stored in the spring is : (block does not slide due to force of
spring.)

µ 2m 2 g 2 2µm2 g2 µ2 m 2 g 2 3µ2mg2
(A) (B) (C) (D)
k k 2k k
D 10. A wedge of mass M fitted with a spring of stiffness ‘k’ is kept on a smooth
horizontal surface. A rod of mass m is kept on the wedge as shown in
the figure. System is in equilibrium and at rest Assuming that all surfaces
are smooth, the potential energy
stored in the spring is :

m g2 tan 2  m2 g tan 2  m2 g2 tan 2  m2 g2 tan 2 

(A) (B) (C) (D)
2K 2K 2K K

D 11. A body of mass m dropped from a certain height strikes a light vertical fixed spring of stiffness k. The height of its
3mg
fall before touching the spring if the maximum compression of the spring is equal to is :
k
3 mg 2 mg 3 mg mg
(A) 2 k (B) (C) 4 K (D) 4 K
k
D 12. A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by
1 m/s so as to have same kinetic energy as that of the boy. The original speed of the man will be
1 1
(A) 2 m/s (B) ( 2 – 1)m/s (C) m/s (D) m/s
( 2  1) 2

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 101
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

D 13. Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically
to stretch the spring by a length x over its natural length. The work done by the spring on each mass during the above
streching is
1 2 1 1 1
(A) kx (B) – kx2 (C) kx2 (D) – kx2
2 2 4 4
D 14. A rod of length 1m and mass 0.5 kg hinged at one end, is initially hanging vertical. The other end is now raised
slowly until it makes an angle 60º with the vertical. The required work is :(use g = 10 m/s 2)
5 5 17 5 3
(A) J (B) J (C) J (D) J
2 4 8 4

SECTION (E) : POWER

E 1. A car of mass ‘m’ is driven with a constant acceleration ‘a’ along a straight level road against a constant external
resistive force ‘R’. When the velocity of the car is ‘V’, the rate at which the engine of the car is doing work will be
(A) RV (B) maV (C) (R + ma)V (D) (ma – R)V

E 2. The average power required to lift a 100 kg mass through a height of 50 metres in approximately 50 seconds would be
(A) 50 J/s (B) 5000 J/s (C) 100 J/s (D) 980 J/s
E 3. A block of mass m is moving with a constant acceleration 'a' on a rough horizontal plane. If the coefficient of
friction between the block and plane is µ.The power delivered by the external agent at a time t from the beginning
is equal to :
(A) ma 2t (B) µmgat (C) µm(a + µg) gt (D) m(a + µg) at

E 4. A particle m oves with a velocity v = (5 î – 3 ĵ + 6 k̂ ) m /s under the influence of a constant force

F = (10 î + 10 ĵ + 20 k̂ )N. The instantaneous power applied to the particle is :
(A) 200 J/s (B) 40 J/s (C) 140 J/s (D) 170 J/s

E 5. An electric motor creates a tension of 4500 N in hoisting cable and reels it at the rate of 2 m/s. What is the power
of electric motor ?
(A) 9 W (B) 9 KW (C) 225 W (D) 9000 H.P.

E 6. A man M1 of mass 80 kg runs up a staircase in 15 s. Another man M2 also of mass 80 kg runs up the stair case
in 20 s. The ratio of the power developed by them (P1 / P2) will be :
(A) 1 (B) 4/3 (C) 16/9 (D) None of the above

SECTION (F) : CONSERVATIVE & NONCONSERVATIVE FORCES AND EQUILIBRIUM

a
b
F-1. The potential energy of a particle in a field is U =  , where a and b are constant. The value of r in terms of
2
r r
a and b where force on the particle is zero will be :
a b 2a 2b
(A) (B) (C) (D)
b a b a

F-2. Potential energy v/s displacement curve for one dimensional conservative
field is shown. Force at A and B is respectively.

(A) Positive, Positive

(B) Positive, Negative
(C) Negative, Positive
(D) Negative, Negative

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 102
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

F-3. The potential energy of a particle varies with distance x as shown in the graph.
The force acting on the particle is zero at
(A) C
(B) B
(C) B and C
(D) A and D.

F-4. The diagrams represent the potential energy U as a function of the inter-atomic distance r. Which diagram corresponds
to stable molecules found in nature.
U

(A) (B) (C) (D)

r
O

F-5. For the path PQR in a conservative force field (fig.), the amount of work done in carrying a
body from P to Q & from Q to R are 5 J & 2 J respectively . The work done
in carrying the body from P to R will be -
(A) 7 J (B) 3 J
(C) 21 J (D) zero

F-6. The potential energy for a force field F is given by U(x, y) = sin (x + y). The force acting on the particle of mass m at
 
 0,  is
 4
1
(A) 1 (B) 2 (C) (D) 0
2
F-7.* A particle is taken from point A to point B under the influence of a force field. Now it is taken back from B to A and
it is observed that the work done in taking the particle from A to B is not equal to the work done in taking it from
B to A. If W nc and W c is the work done by non-conservative forces and conservative forces present in the system
respectively, U is the change in potential energy, k is the change in kinetic energy, then
(A) W nc – U = k (B) W c = – U (C) W nc + W c = k (D) W nc – U = –k

Part - III
1. Statement -1 : A person walking on a horizontal road with a load on his head does no work on the load against
gravity.
Statement -2 : No work is said to be done, if directions of force and displacement of load are perpendicular to
each other.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
2. Statement-1 : The instantaneous power of an agent is measured as the dot product of instantaneous velocity
and the force (only one force applied by agent) acting on it at that instant.
Statement-2 : The unit of instantaneous power is watt.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 103
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
3. Statement-1 : Water at the foot of the water fall is usually at different temperature from that at the top.
Statement-2 : Some part of the potential energy of water at the top is converted into heat energy at the foot of
the water fall.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

4. Statement-1 : Graph between potential energy of a spring versus the extension or compression of the spring is
a straight line.
Statement-2 : Potential energy of a stretched or compressed spring is proportional to square of extension or
compression.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

EXERCISE # 2
Single choice type
1. The work done by all the forces on a system equals the change in
(A) total energy (B) kinetic energy (C) potential energy (D) none of these

2. A small block of mass m is kept on a rough inclined surface of inclination  fixed in a elevator. The elevator goes down
with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block
with respect to ground in time t will be
(A) zero (B) –mgvt cos2 (C) –mgvt sin2 (D) mgvt sin2

3. You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase depends on (k = 0)

(A) the path taken by the suitcase (B) the time taken by you in doing so
(C) the weight of the suitcase (D) your weight.

4. A block of mass M is hanging over a smooth and light pulley through a light string. The other end of the string is pulled
by a constant force F. The kinetic energy of the block increases by 20 J in 1s.
(A) the tension in the string is Mg
(B) the tension in the string is F
(C) the work done by the tension on the block is 20 J in the above 1 s.
(D) the work done by the force of gravity is – 20 J in the above 1s.
5. In the figure a block slides along a track from one level to a higher level, by moving through an intermediate valley.
The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a
distance d. The block’s initial speed v0 is 6m/s, the height difference h is 1.1 m and the coefficient of kinetic
friction µ is 0.6. The value of d is :

(A) 1.17 m (B) 1.71 m (C) 7.11 m (D) 11.7 m

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 104
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
6. A small particle slides along a track with elevated ends and a flat central part, as shown in figure. The flat part
has a length 3m. the curved portions of the track are frictionless, but for the flat part the coefficient of kinetic
friction is µ = 0.2. The particle is released at point A, which is at a height h = 1.5 m above the flat part of the track.
The position where the particle finally come to rest is:
(A) left to mid point of the flat part A
(B) right to the mid point of the flat part
(C) Mid point of the flat part h

(D) None of these

3.0m

7. A block of mass 50 kg is projected horizontally on a rough horizontal floor. The coefficient of friction between the
block and the floor is 0.1. The block strikes a light spring of stiffness k = 100 N/m with a velocity 2m/s. The
maximum compression of the spring is :

(A) 1 m (B) 2 m (C) 3 m (D) 4 m

8. A car of mass m starts moving so that its velocity varies according to the law v =  s , where  is a constant, and
s is the distance covered. The total work performed by all the forces which are acting on the car during the first
t seconds after the beginning of motion is
(A) m 4 t2/8 (B) m 2 t4/8 (C) m 4 t2/4 (D) m 2 t4/4

9. A block of mass 250 g is kept (does not sticks to spring) on a vertical spring of spring constant 100 N/m fixed from
below (block is in equilibrium). The spring is now compressed to have a length 10 cm shorter than its natural length and
the system is released from this position. How high does the block rise from this
position ? Take g = 10 m/s2.
(A) 20 cm (B) 30 cm (C) 40 cm (D) 50 cm

10. In a projectile motion, KE varies with time as in graph : (   0, 180º with vertical)

(A) (B) (C) (D)

11. An open knife edge of mass ‘m’ is dropped from a height ‘h’ on a wooden floor. If the knife penetrates upto depth ‘d’ into
the wood, the average resistance offered by the wood to the knife edge is
2
 h  h  h
(A) mg (B) mg  1   (C) mg  1   (D) mg  1  
 d  d  d
12. The potential energy of a system is represented in the first figure, the force acting on the system will be represented by

F(x)
F(x)

a
(A) (B) (C) x (D)
a x

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 105
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
13. Which of the following graphs is correct for kinetic energy (E) and potential energy (U) with height (h) from the ground
for a projectile motion of the particle on a horizontal ground (h << R E and U = 0 at h = 0)

(A) (B) (C) (D)

1
14. The graph between E and is (E = kinetic energy and p = momentum)
p

(A) (B) (C) (D)

15. The force acting on a body moving along x-axis varies with the position of the particle as shown in the figure.

The body is in stable equilibrium at

(A) x = x1 (B) x = x2 (C) both x1 and x2 (D) neither x1 nor x2
16. The graph between kinetic energy E and velocity v is :

(A) (B) (C) (D)

17. A 10 kg small block is pulled in the vertical plane along a frictionless surface in the
form of an arc of a circle of radius 10 m. The applied force is of 200 N as shown in the
figure. If the block started from rest at A, the speed
at B would be: (g = 10 m/s2)
(A) 3 m/s (B) 10 3 m/s
(C) 100 3 m/s (D) None of these

18. The total work done on a particle is equal to the change in its kinetic energy
(A) if only conservative forces are acting
(B) if only non-conservative forces are acting
(C) if both conservative and nonconservative forces are acting
(D) none of these

19. A force F  K ( y î  x ĵ ) where K is a positive constant, acts on a particle moving in the x-y plane. Starting from
the origin, the particle is taken along the positive x-axis to the point (a,0) and then parallel to the y-axis to the

point (a,a). The total work done by the force F on the particle is
(A) –2Ka 2 (B) 2Ka2 (C) –Ka2 (D) Ka2
20. In the figure the variation of components of acceleration of a particle of mass 1 kg is shown w.r.t. time. The initial

velocity of the particle is u  ( 3 î  4 ĵ ) m/s. The total work done by the resultant force on the particle in time
interval from t = 0 to t = 4 seconds is :

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 106
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

(A) 22.5 J (B) 10 J (C) 0 (D) None of these

21. Select the correct alternative.

(A) Work done by kinetic friction on a body always results in a loss of its kinetic energy.
(B) Work done on a body, in the motion of that body over a close loop is zero for every force in nature.
(C) Total mechanical energy of a system is always conserved no matter what type of internal and external forces
on the body are present.
(D) When total work done by a conservative force on the system is positive then the potential energy associated
with this force decreases.

More than one choice type

22.* A heavy stone is thrown from a cliff of height h in a given direction. The speed with which it hits the ground
(A) must depend on the speed of projection (B) must depend on angle of projection
(C) must depend on height h of the cliff (D) may be smaller than the speed of projection
23.* No work is done by a force on an object if
(A) the force is always perpendicular to its velocity
(B) the force is always perpendicular to its acceleration
(C) the object has no motion but the point of application of the force moves on the object
(D) the object moves in such a way that the point (of the body) of application of the force remains fixed.
24.* The kinetic energy of a particle continuously increases with time
(A) the resultant force on the particle must be parallel to the velocity at all instants.
(B) the resultant force on the particle must be at an angle less than 90° with the velocity all the time
(C) its height above the ground level must continuously decrease
(D) the magnitude of its linear momentum is increasing continuously
25*. One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth
1
horizontal surface. In a displacement , the work done by the spring is kx2. The possible cases are
2
(A) the spring was initially compressed by a distance x and was finally in its natural length
(B) it was initially stretched by a distance x and finally was in its natural length
(C) it was initially in its natural length and finally in a compressed position
(D) it was initially in its natural length and finally in a stretched position

Matrix Match Type

1. A block A of mass m kg lies on block B of mass m kg. B in turn lies on smooth horizontal plane. The coefficient of
friction between A and B is . Both the blocks are initially at rest. A horizontal force F is applied to lower block B at t =
0 such that there is relative motion between A and B. In the duration from t = 0 second till the lower block B undergoes
a displacement of magnitude L, match the statements in column-I with results in column-II.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 107
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
Column-I Column-II
(A) Work done by friction force on block A is (p) positive
(B) Work done by friction force on block B is (q) negative
(C) Work done by friction on block A plus (r) less than mgL in magnitude
work done by friction on block B is
(D) Work done by force F on block B is (s) equal to mgL in magnitude
2. A block of mass m lies on wedge of mass M. The wedge in turn lies on smooth horizontal surface. Friction is
absent everywhere. The wedge block system is released from rest. All situation given in column-I are to be
estimated in duration the block undergoes a vertical displacement 'h' starting from rest (assume the block to be
still on the wedge). Match the statement in column-I with the results
in column-II. (g is acceleration due to gravity)

Column I Column II
(A) Work done by normal reaction acting (p) positive
on the block is
(B) Work done by normal reaction (exerted (q) negative
by block) acting on wedge is
(C) The sum of work done by normal reaction (r) zero
on block and work done by normal
reaction (exerted by block) on wedge is
(D) Net work done by all forces on block is (s) less than mgh in magnitude

Comprehension Type

Comprehension # 1
In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate.
The particle moves under the effect of this conservative force along the x-axis.

U(in J)
20
15
10
-5 5
X (in metre)
-10 2 10

12
-15

1. If the particle is released at the origin then :

(A) it will move towards positive x-axis.
(B) it will move towards negative x-axis.
(C) it will remain stationary at the origin.
(D) its subsequent motion cannot be decided due to lack of information.
2. If the particle is released at x = 2 +  where   0 (it is positive) then its maximum speed in subsequent motion
will be :
(A) 10 m/s (B) 5 m/s (C) 5 2 (D) 7.5 m/s

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 108
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
3. x = – 5 m and x = 10 m positions of the particle are respectively of
(A) neutral and stable equilibrium. (B) neutral and unstable equilibrium.
(C) unstable and stable equilibrium. (D) stable and unstable equilibrium.
Comprehension # 2
Ram and Ali are two friends. Both work in a factory. Ali uses a camel to transport the load within the factory.
Due to low salary & degradation in health of camel, Ali becomes worried and meets his friend Ram and discusses
his problem. Ram collected some data & with some assumptions concluded the following.

(i) The load used in each trip is 1000 kg and has friction coefficient  k = 0.1 and  s = 0.2.
(ii) Mass of camel is 500 kg.
(iii) Load is accelerated for first 50 m with constant acceleration, then it is pulled at a constant speed of 5m/s for
2 km and at last stopped with constant retardation in 50 m. (String used for pulling load is almost horizontal).
4. Sign of work done by the camel on the load during parts of motion : accelerated motion, uniform motion and
retarted motion respectively are :
(A) +ve, + ve, +ve (B) +ve, +ve, – ve (C) +ve, zero, – ve (D) +ve, zero, +ve
5. The ratio of magnitude of work done by camel on the load during accelerated motion to retarded motion is :
(A) 3 : 5 (B) 2.2 : 1 (C) 1 : 1 (D) 5 : 3
6. Maximum power transmitted by the camel to load is :
(A) 6250 J/s (B) 5000 J/s (C) 105 J/s (D) 1250 J/s
EXERCISE # 3
JEE Advanced & IIT JEE Archive
* Marked Questions may have more than one correct option.
1. A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which
varies with the distance x of the particle from the origin as F(x) = –kx + ax3. Here k and a are positive constants.
For x  0, the functional form of the potential energy U(x) of the particle is [JEE(Scr) 2002, 3/105]

(A) (B) (C) (D)

2. An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end.
The mass is released with the spring initially unstreched. Then the maximum extension in the spring is
[JEE(Scr) 2002, 3/105]
(A) 4 Mg/k (B) 2 Mg/k (C) Mg/k (D) Mg/2k
3. A particle moves under the influence of a force F = kx in one dimensions (k is a positive constant and x is the
distance of the particle from the origin). Assume that the potential energy of the particle at the origin is zero, the
schematic diagram of the potential energy U as a function of x is given by [JEE(Scr) 2004, 3/84]

(A) (B) (C) (D)

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 109
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

4. STATEMENT - 1 : [JEE 2007' 3/184]

A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the
block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30º with the
horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the
mechanical energy in the second situation is smaller than that in the first situation.
Because
STATEMENT - 2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
5. A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4 k, respectively (see figure
). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports
have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x
(figure ) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are
y
measured with respect to the equilibrium position of the block B. The ratio is [JEE 2008, 3/163]
x
Figure :

1 1
(A) 4 (B) 2 (C) (D)
2 4

6. A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses
0.36 kg and 0.72 kg. Taking g = 10 m/s2, find the work done (in joules) by the string on the block of mass 0.36 kg
during the first second after the system is released from rest. [ JEE 2009, 4/160, –1]

7. A block of mass 2 kg is free to move along the x–axis. It is at rest and from t = 0 onwards, it is subjected to a time–
dependent force F(t) in the x–direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block
after 4.5 s is:– F(t) [JEE 2010]
4N

4.5 s
O 3s t

(A) 4.50 J (B) 7.50 J (C) 5.06 J (D) 14.06 J

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 110
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
8. A block of mass 0.18 kg is attached to a spring of force constant 2 N m –1. The coefficient of friction between the block
and the floor is 0.1. Initially the block is at rest and the spring is unstretched. An impulse is given to the block as shown
in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block
in m s–1 is V = N/10. Then N is. [IIT–JEE 2011]

 x ˆi  y ˆj  (K being the constant of appropriate

9. The work done on a particle of mass m by a force K  2 2 3/ 2 
 (x  y ) (x  y 2 )3 / 2
2


dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the
origin in the x–y plane is:– [JEE Advanced 2013]

2Kx Kx Kx
(A) (B) (C) (D) 0
a a 2a

10. A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface.
The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the
following sketches describes the variation of its kinemetic energy K with time t most appropriately? The figures are only
illustrative and not to the scale. [JEE Advanced 2013]

K K K K

(A) (B) (C) (D)

t t t t

Comprehension Type for Q. 11 & 12.

A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The
block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous
velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, is 150 J. (Take the
acceleration due to gravity, g = 10 ms–2) [JEE Advanced 2013]

R P

Q R

11. The speed of the block when it reaches the point Q is:–

(A) 5 ms–1 (B) 10 ms–1 (C) 10 3 ms–1 (d) 20 ms–1

12. The magnitude of the normal reaction that acts on the block at the point Q is:–
(A) 7.5 N (B) 8.6 N (C) 11.5 N (D) 22.5 N

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 111
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
13. A bob of mass m, suspended by a srting of length l1, is given a minimum velocity required to complete a full circle in the
vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2,
which is initially at rest. Both the strings are mass–less and inextensible. If the second bob, after collision, acquires the
minimum speed required to complete a full circle in the vertical plane, the ratio l 1/l2 is. [JEE Advanced 2013]
14. A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle.
If the initial speed (in m/s) of the particle is zero, the speed (in m s–1) after 5s is [JEE Advanced 2013]

15. Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is
pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming
no frictional losses, the kinetic energy of the block when it reaches Q is (n × 10) joules. The value of n is (take
acceleration due to gravity = 10 ms–2) Q [JEE Advanced 2014]

4m
90o
O 3m P
16. A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed
vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire
without friction. As the bead moves from A to B, the force is applies on the wire is.
A
[JEE Advanced 2014]

90o B

(A) always radially outwards (B) always radially inwards

(C) radially outwards initially and radially inwards later (D) radially inwards initially and radially outwards later

17. A particle of unit mass is moving along the x–axis under the influence of a force and its total energy is conserved.
(  and U0 are constants). Match the potential energies in column I to the corresponding statement(s) in column II.
Column I Column II [JEE Advanced 2015]

2 2
U0   x  
(A) U1 (x)  1   (p) the force acting on the particle is zero at x = a.
2   a  

2
U0  x 
(B) U2 (x)  (q) the force acting on the particle is zero at x = 0.
2  a 

2
U0  x    x 2 
(C) U3 (x)  exp     (r) the force acting on the particle is zero at x = –a.
2  a    a  

U0  x 1  x 3 
(D) U4 (x)       (s) The particle experiences an attractive force towards x = 0 in
2  a 3  a  

the region |x| < a.

U0
(t) The particle with total energy can oscillate about the point x = –a
4
Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 112
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
JEE Main & AIEEE Archive
1. If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before
coming to rest? [AIEEE 2002, 4/300]
(1) 1 cm (2) 2 cm (3) 3 cm (4) 4 cm

2. A spring of force constant 800 N/m has an extension of 5cm. The work done in extending it from 5cm to 15cm is
(1) 16 J (2) 8 J (3) 32 J (4) 24 J [AIEEE 2002, 4/300]

3. A spring of spring constant 5 × 103 N/m is stretched initially by 5 cm from the unstretched position. Then the work
required to stretch it further by another 5 cm is : [AIEEE 2003, 4/300]
(1) 12.50 N-m (2) 18.75 N-m (3) 25.00 N-m (4) 6.25 N-m

4. A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The
total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?
(1) 7.2 J (2) 3.6 J (3) 120 J (4) 1200 J
[AIEEE 2004, 4/300]
 
5. A force F  (5 î  3 ĵ  2k̂ ) N is applied over a particle which displaces it from origin to the point r  ( 2 î  ˆj ) m . The work
done on the particle in joules is : [AIEEE 2004, 4/300]
(1) – 7 (2) + 7 (3) + 10 (4) + 13
6. A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the
body as a function of time, is given by : [AIEEE 2005, 4/300]
mv 2 mv 2 1 mv 2 1 mv 2 2
(1) 2 .t (2) 2 .t2 2 (3)
.t (4) .t
T T 2 T 2 T2
7. A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. the work done by the force of gravity during
the time the particle goes up is [AIEEE 2006, 1.5/180]
(1) – 0.5 J (2) –1.25 J (3) +1.25 J (4) 0.5 J

8. A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying
the force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s2
[AIEEE 2006, 3/180]
(1) 22 N (2) 4 N (3) 16 N (4) 20 N

9. A particle is projected at 60º to the horizontal with a kinetic energy K. The kinetic energy at the highest point is
[AIEEE 2007, 3/120]
(1) K (2) zero (3) K/4 (4) K/2

10. An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in
the range [AIEEE 2008, 3/105]
(1) 2 × 105 J – 3 × 105 J (2) 20,000 J – 50,000 J
(3) 2,000 J – 5,000 J (4) 200 J – 500 J

11. The potential energy function for the force between two atoms in a diatomic molecules is approximately given by
a b
U(x)  12
 6 , where a and b are constants and x is the distance between the atoms. If the dissociation energy
x x
of the molecule is D = [U(x  )  Uat equilibrium ] , D is:– [JEE-MAIN – 2010]

b2 b2 b2 b2
(1) (2) (3) (4)
2a 12a 4a 6a

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 113
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
12. This question has Statement I and Statement II. Of the four choice given after the statements, choose the one that best
describes the two statements. [JEE-MAIN – 2012]
If two springs S1 and S2 of force constant k1 and k2, respectively, are stretched by the same force, it is found that more
work is done on spring S1 than one spring S2.
Statement I : If stretched by the same amount, work done on S1, will be more than that on S2.
Statement II : k1 < k2.
(1) Statement I is false, Statement II is true
(2) Statement I is true, Statement II is false
(3) Statement I is true, Statement II is true, Statement II is the correct explanation for Statement I
(4) Statement I is true, Statement II is true, Statement II is not the correct explanation for Statement I

13. At time t = 0s a particle starts moving along the x-axis. If its kinetic energy increases uniformly with time ‘t’, the net
force acting on it must be proportional to : [AIEEE 2011 (11-05-2011)]
1
(1) constant (2) t (3) (4) t
t

14. When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx2 where a and b
are constants. The work done in stretching the unstretched rubber-band by L is :
[JEE-MAIN – 2014]
aL2 bL3 1  aL2 bL3  1
(1)  (2) 2  2  3  (3) aL2 + bL3 (4) (aL2  bL3 )
2 3   2
15. A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of
friction, between the particle and the rough track equals  . The particle is released, from rest, from the point P and it
comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each
other, and no energy is lost when particle changes direction from PQ to QR.
The values of the coefficient of friction  and the distance x(=QR), are, respectively close to :
[MAIN – 2016]

(1) 0.2 and 6.5 m (2) 0.2 and 3.5 m (3) 0.29 and 3.5 m (4) 0.29 and 6.5 m
16. A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the
potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work
done only when the weight is lifted up ? Fat supplies 3.8 × 107 J of energy per kg which is converted to mechanical
energy with a 20% efficiency rate. Take g=9.8 ms–2: [JEE-MAIN – 2016]
(1) 2.45 × 10–3 kg (2) 6.45 × 10–3 kg (3) 9.89 × 10–3 kg (4) 12.89 × 10–3 kg
17. A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its intial speed is

1
v0 = 10 ms–1. If, after 10 s, its energy is mv02, the value of k will be:- [JEE-MAIN – 2017]
8
(1) 10–4 kg m –1 (2) 10–1 kg m –1 s–1 (3) 10–3 kg m –1 (4) 10–3 kg s–1
18. A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the
force during the first 1 sec. will be : [JEE-MAIN – 2017]
(1) 9 J (2) 18 J (3) 4.5 J (4) 22 J

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 114
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
19. A particle of mass m is intially at rest at the origin. It is subjected to a force and starts moving along the X-axis. Its
kinetic energy K changes with time as dK/dt = t,where  is a positive cosntant of appropriate dimensions. Which of
the following statements is (are) true ?
(1) The force appliced on the particles cosntant
(2) The speed of the particle is proportional to time
(3) The speed of the particle from the origin increases linearly with time
(4) The force conservative [JEE-Advanced – 2018]

EXERCISE # 4
Part - I
Single choice type
 
1.    
A force F = 3 t î  5 ĵ N acts on a body due to which its position varies as s = 2 t 2 î  5 ĵ . Work done by this force in
first two seconds is:
(A) 23 J (B) 32 J (C) zero (D) can't be obtained
2. The force exerted by a compression device is given by F(x) = kx (x – ) for 0 < x <  , where  is the maximum
possible compression, x is the compression and k is a constant. The work required to compress the device by a
distance d will be maximum when :
  
(A) d = (B) d = (C) d = (D) d = 
4 2 2
3. The ratio of work done by the internal forces of a car in order to change its speed from 0 to V and from V to 2V is
(Assume that the car moves on a horizontal road) -
(A) 1 (B) 1/2 (C) 1/3 (D) 1/4
4. A block attached to a spring, pulled by a constant horizontal force, is kept on a
smooth surface as shown in the figure. Initially, the spring is in the natural state. Then
the maximum positive work that the applied force F can
do is : [Given that spring does not break]

F2 2F 2 F2
(A) (B) (C)  (D)
K K 2K
5. The spring block system lies on a smooth horizontal surface. The free end of
the spring is being pulled towards right with constant speed v0 = 2m/s. At t =
0 sec, the spring of constant k = 100 N/cm is unstretched and the block has
a speed 1 m/s to left. The
maximum extension of the spring is
(A) 2 cm (B) 4 cm
(C) 6 cm (D) 8 cm
6. As shown if figure a body of mass 1 kg is shifted from A to D on inclined planes by applying a force slowly such
that the block is always in contact with the plane surfaces. Neglecting the jerk experienced at points C and B,
total work done by the force is :

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 115
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

(A) 90 J (B) 56 J (C) 180 J (D) 0 J

1
7. The potential energy of a particle of m ass m free to move along x-axis is given by U = kx2
2
for x < 0 and U = 0 for x  0 (x denotes the x-coordinate of the particle and k is a positive constant). If the total
2E
mechanical energy of the particle is E, then its speed at x = – is
k
2E E E
(A) zero (B) (C) (D)
m m 2m
8. A chain of mass M and length  is held vertically such that its bottom end just touches the surface of a horizontal table.
The chain is released from rest. Assume that the portion of chain on the table does not form a heap. The momentum of

the portion of the chain above the table after the top end of the chain falls down by a distance .
8

3 3 7 9
(A) M g (B) M g (C) M g (D) M g
14 16 16 14

9. The figure shows a hollow cube of side 'a' of volume V. There is a

V
small chamber of volume in the cube as shown. This chamber is
4
completely filled by m kg of water. Water leaks through a hole H
and spreads in the whole cube. Then the work done by gravity in this
process assuming that the complete water finally lies at the bottom
of the cube is :
1 3
(A) mg a (B) mg a
2 8
5 1
(C) mga (D) mga
8 8
10. Force acting on a particle m oving in a straight line varies with the velocity v of the particle as
K
F= , where K is a constant. The work done by this force in time t is
v

K 2Kt
(A) t (B) 2Kt (C) Kt (D)
v2 v2

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 116
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
11. Power versus time graph for a given force is given below. Work done by the force upto time t( t0).

(A) First decreases then increases (B) First increases then decreases
(C) Always increases (D) Always decreases

12. A pump motor is used to deliver water at a certain rate from a given pipe. To obtain “n” times water from the same
pipe in the same time, the factor by which the power of the motor should be increased is:
(A) n 2 (B) n 3 (C) n4 (D) n1/2
13. An engine pumps up 1000 kg of coal from a mine 100 m deep in 50 sec. The pump is running with diesel and efficiency
of diesel engine is 25%. Then its power consumption will be (g = 10m/sec2):
(A) 10 k W (B) 80 kW (C) 20 kW (D) 24 kW
14. An engine can pull 4 coaches at a maximum speed of 20 m/s. Mass of the engine is twice the mass of every coach.
Assuming resistive forces to be proportional to the weight, approximate maximum speeds of the engine when it pulls 12
and 6 coaches are (power of engine remains constant) :
(A) 8.5 m/s and 15 m/s respectively (B) 6.5 m/s and 8 m/s respectively
(C) 8.5 m/s and 13 m/s respectively (D) 10.5 m/s and 15 m/s respectively

15. A man is supplying an instantaneous power of 500 J/s to a massless string by

pulling it at an instantaneous speed of 10 m/s as shown. It is known that kinetic
energy of the block is increasing at a rate of 100 J/s at
that instant. Then the mass of the block is :
(A) 5 kg (B) 3 kg
(C) 10 kg (D) 4 kg

Multiple Choice Type

16. The given plot shows the variation of U, the potential energy of interaction between two particles with the distance
separating them is r. Then which of the following statements is / are correct.

(A) B and D are equilibrium points

(B) C is a point of stable equilibrium
(C) The force of interaction between the two particles is attractive between points C and D and repulsive between
points D and E on the curve.
(D) The force of interaction between the particles is repulsive between points E and F on the curve.
Part - II
1. A small block of mass 20 kg rests on a bigger block of mass 30 kg, which lies on a smooth horizontal plane.
Initially the whole system is at rest. The coefficient of friction between the blocks is 0.5. A horizontal force
F = 50 N is applied on the lower block.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 117
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

(a) Find the work done by frictional force on upper block and on the lower block in t = 2sec.
(b) Is the magnitude of work done by frictional force on upper and lower block same?
(c) Is the work done by frictional force on upper block converted to heat or mechanical energy or both?
2. A block of mass ' m ' is pushed against a spring of spring constant ' k ' fixed at one end to a wall. The block can
slide on a frictionless table as shown in the figure. The natural length of the spring is L 0 and it is compressed to
one-fourth of natural length and the block is released. Find its velocity as a function of its distance (x) from the
wall and maximum velocity of the block. The block is not attached to the spring.

3. A block of mass m rests on a rough horizontal plane having coefficient of kinetic friction µ k and coefficient of static
5  k mg
friction µs. The spring is in its natural length, when a constant force of magnitude P = starts acting on the
4
block. The spring force F is a function of extension x as F = kx3. (Where k is spring constant)

(a) Comment on the relation between µs and µk for the motion to start.
(b) Find the maximum extension in the spring (Assume the force P is sufficient to make the block move).

4. A spring (k = 100 Nm–1) is suspended in vertical position having one end fixed at top & other end joined with a 2kg block.
When the spring is in non deformed shape, the block is given initial velocity 2 m/s in downward direction. Find maximum
elongation of the spring.

5. A small block slides along a path that is without friction until the block reaches the section L = 3m, which begins
at height h = 3m on a flat incline of angle 37°, as shown. In that section, the coefficient of kinetic friction is 0.50.
The block passes through point A with a speed of 136 m/s. Find the speed of the block as it passes through
point B where the friction ends, in m/s. (Take g = 10 m/s2 )

6. As shown in the figure, there is no friction between the horizontal surface and the lower block (M = 3 kg) but friction
coefficient between both the blocks is 0.2. Both the blocks move together with initial speed V towards the spring,
compresses it and due to the force exerted by the spring, moves in the reverse direction of the initial motion. What can
be the maximum value of V (in cm/s) so that during the motion, there is no slipping between the blocks (use g = 10 m/
s2).

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 118
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

m
K=400N/m 1kg =0.2
M
3kg

smooth
7. In the figure shown, a spring of spring constant K is fixed at one end and the other end is attached to the mass ‘m’. The
coefficient of friction between block and the inclined plane is ‘’. The block is released when the spring is in its natural
length. Assuming that tan  >  find the maximum speed of the block during the motion.

8. A block of mass ' m ' is attached to one end of a massless spring of spring constant ' k '. The other end of the spring is
fixed to a wall. The block can move on a horizontal rough surface. The coefficient of friction between the block and the
2  mg
surface is . The block is released when the spring has a compression of . Find:
k

(i) Maximum speed of the block.

(ii) Will the block have velocity towards left during its motion? If yes, then find the extension in the spring at that time.

9. A particle of mass m = 1 kg lying on x-axis experiences a force given by law


F = x (3x – 2) î Newton,
where x is the x-coordinate of the particle in meters.

(a) Locate the points on x-axis where the particle is in equilibrium.

(b) Draw the graph of variation of force F (y-axis) with x-coordinate of the particle (x-axis).
Hence or otherwise indicate at which positions the particle is in stable or unstable equilibrium.
(c) What is the minimum speed to be imparted to the particle placed at x = 4 meters such that it reaches the origin.

10. The potential energy (in S units) of a particle of mass 2 kg in a conservative field is U = 6x – 8y. If the initial velocity of

the particle is u = – 1.5 î + 2 ĵ then find the total distance travelled by the particle in first two seconds.

11. A particle of m ass 2kg starts to move at position x = 0 and tim e t = 0 under the action of force
F(10 + 4x) N along the x-axis on a frictionless horizontal track. Find the power delivered by the force in watts at
the instant the particle has moved by the distance 5m.

12. A ball is projected from the ground at an angle of 45 0 with the horizontal surface. It reaces a maximum height of
120 m and returns to the ground. Upon hitting the ground for th first time, it loses half of its kinetic energy.
Immediately after the bounce, the velocity of the ball makes an angle of 300 with horizontal surface. The maximum
height it reaches after the bounce, in metres, is ....... [JEE- Advanced -2018]

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 119
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy

ANSWERS
(viii) Compare W and W 1 with K and K1, they are
Exercise # 1 respectively equal.
PART - I (ix) The work - energy theorem holds for moving
observers.
SECTION (A)
SECTION (D)
A 1. (a) zero (b) zero (c) –mgvt (d) mgvt
D 1. 10 33 m/s D 2. 0.082 J
A 2. 2000 J A 3. (i) Zero (ii) 500J
7
A 4. 150 J D 3. m s–1 = 1.40 m s–1 D 4. 6 m s–1 .
5
A 5. At a horizontal distance of 1 m from the end of the track. D 5. 2 g = 19.6 J D 6. 0.7 g2 = 70J
1
A 6. 8J A 7. (a) 640 J (b) 640J D 7.
8
SECTION (B) SECTION (E)
575 8
B 1. 135 J. B 2. J = 287.5 J E 1. hp E 2. 320 hp E 3. 50 W
2 3
E 4. 1600 W E 5. 700 W E 6. 1200 kg
–2
mg
B 3. 8 × 10 J B 4. 100
2 E 7. 8 second E 8. HP
1119
SECTION (C)
E 9. 2 min
9 –1
C 1. = 0.5625 J C 2. vf = 20 10 = 63.2 ms SECTION (F)
16

35 a5
C 3. – J = – 8.75 J C 4. F = 6300 N F 1. (a) No (b) W ABC = W ADC = (J),
4 3
C 5. 80 kg C 6. 4000 J
2a 5
C 7. (a) 875 Joule (b) –250 joule (c) 625 joule. W AC = (J)
5
(d) 625 joule, Change in kinetic energy of the body is
equal to the work done by the net force in 10 second. dU
This is in accordance with work-energy theorem. F 2. (a) F = – =
dy
15mv 2
C 8. 10 m s–1 C 9.
16 x 2 (b) F = –
dU
=3ay2 + 2by
C-10. 4mg/k dy
C-11. (a) Since the gravitational force is a conservative force
therefore the work done in round trip is zero. dU
(c) F = – = – U 0cosy
(b) wF = (9.8) (0.3)(1/2)(1+0.15 3 ) (10) J  18.519 J dy

(c) –0.15 × 0.3 × 9.8 × ( 3 /2) × 20 J  – 7.638 J F 3. F  ( 4 î  36 ĵ  2k̂ ) N
(d) 0.3 × 9.8 × (10/2) (1 – 0.15 × 3 )  10.880 J F 4. (i) U(x, y, z) = (–2x – 3y)
C 12.  = 0.245 C-13. – 2 J (ii) U(x, y, z) = – (x2 + y2)
C-14. (i) a1 = F/m, so v1 = a1t = Ft/m. (iii) U(x, y, z) = – xy.
(ii) Since velocities add, v = vc + v1 = vc + Ft/m
(iii) K1 = m(v1)2/2 = F2t2/2m PART - II
(iv) K = m (vc + v1)2/2 – mvc2/2 SECTION : (A)
(v) s1 is a1t2/2 = Ft2/2m A 1. B A 2. A A 3. C A 4. C
(vi) s1 + vct A 5. B A 6. B A 7. C A 8. A
1 F 2 1 F 2 A 9. C A 10. A A 11. ABC A 12. ABC
(vii) Wg = F [Vc t + t ], W t = F [ t ] A 13.*BC A 14. BD A 15. ABC
2 m 2 m

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 120
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
SECTION (B) : 11. (B) 12. (A) 13. (5)
B 1. B B 2. C B 3. D B 4. D 14. (5) 15. (5) 16. (D)
B 5. A 17. [(A – p, q, r, t); (B – q, s); (C – p, q, r, s); (D – p, r, s)]
JEE Main & AIEEE Archive
SECTION (C) : 1. 1 2. 2 3. 2
C 1. A C 2. B C 3. D C 4. D 4. 2 5. 2 6. 1
C 5. A C 6. A C 7. D C 8. B 7. 2 8. 1 9. 3
C 9. D C 10. A C 11. A C 12. A 10. 3 11. 3 12. 1
C 13. C 13. 3 14. 1 15. 3
16. 4 17. 1 18. 3 19. (1, 2)
SECTION (D) :
D 1. C D 2. A D 3. C D 4. A EXERCISE # 4
D 5. B D 6. C D 7. A D 8. D Part - I
D 9. C D 10. C D 11. A D 12. C 1. B 2. D 3. C
D 13. D D 14. B 4. B 5. C 6. A
7. A 8. C 9. C
SECTION (E) : 10. C 11. C 12. B
E 1. C E 2. D E 3. D E 4. C 13. B 14. A 15. D
E 5. B E 6. B 16. BD
SECTION (F) : PART - II
F-1. C F-2. B F-3. C F-4. A
F-5. A F-6. A F-7. ABC 2
k   3 L0  2

2. v=     L 0  x  when x< L0
PART - III m  4  

1. A 2. B 3. A 4. D
3 L0 k
; vmax = when x  L0
EXERCISE # 2 4 m
Single choice type   K mg 
1/ 3

1. B 2. C 3. C 4. B 3. (a) 5k > 4s ; (b) x =  

 K 
5. A 6. C 7. A 8. A
9. A 10. B 11. C 12. C  3  1
 
13. A 14. C 15. B 16. A 4. x = 5  m 5. 4 6. 20
17. B 18. C 19. C 20. B  
21. D
More than one choice type m
8. (i)  g (ii) No
22. AC 23. ACD 24. BD 25. AB k

Matrix Match Type 2

9. (a) x = 0 and x = m
1. (A) p, r (B) q, s (C) q, r (D) p 3

2. (A) q, s (B) p, s (C) r, s (D) p, s

Comprehension Type (b)

1. B 2. B 3. D 4. A
5. D 6. A The particle is in stable equilibrium at x = 0 metre and

EXERCISE # 3 2
unstable equilibrium at x = metre
3
JEE Advanced & IIT JEE Archive
1. D 2. B 3. A 2600
(c) v= m/s
4. C 5. 6. 7. (C) 27
8. (4) 9. (D) 10. (B) 10. 15 m. 11. 300 12. 30m

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 121
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694
 Work Power Energy
EXERCISE # 1
Part - I
SECTION (A) : KINEMATICS OF CIRCULAR MOTION
A 1. Figure shows a circular path taken by a particle. If the instantaneous velocity of the particle is

v = (2m /s) î – (2 m/s) ĵ . Through which quadrant is the particle moving when it is travelling (a) clockwise and (b)
counter clockwise around the circle? y

A 2. Find the ratio of angular speeds of minute hand and hour hand of a watch and also find the angular speed of the
second's hand in a watch.

A 3. A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first
2 seconds, it rotates through an angle 1. In the next 2 seconds, it rotates through an additional angle 2. find the
ratio of 2/1 .

A 4. If the equation for the angular displacement of a particle moving on a circular path is given by () = 2t3 + 0.5, where  is
in radians and t in seconds, then find the angular velocity of the particle after 2 seconds from its start.

A 5. The length of second’s hand in a watch is 1 cm. Find the magnitude of change in velocity of its tip in 15 seconds.
Also find out the magnitude of average acceleration during this interval.

SECTION (B) : RADIAL AND TANGENTIAL ACCELERATION

B 1. A particle moves uniformly in a circle of radius 25 cm at two revolution per second. Find the acceleration of the
particle in m/s2 .

B 2. A car is moving with speed 30 m/sec on a circular path of radius 500 m. Its speed is increasing at the rate of 2
m/sec 2. What is the acceleration of the car at that moment?
B3 A particle moves in a circle of radius 1.0 cm at a speed given by v= 2.0 t where v is in cm/s and t in seconds.
(a) Find the radial acceleration of the particle at t = 1s.
(b) Find the tangential acceleration at t = 1s
(c) Find the magnitude of the acceleration at t = 1s.

SECTION (C) : CIRCULAR MOTION IN HORIZONTAL PLANE

C 1. A small sphere of mass 200 gm is attached to an inextensible string of length 130 cm whose upper end is fixed
to the ceiling. The sphere is made to describe a horizontal circle of radius 50 cm. Calculate the time period of
this conical pendulum and the tension in the string.
1
C 2. A mosquito is sitting on an L.P. record of a gramophone disc rotating on a turn table at 33 revolution per
3
minute. The distance of the mosquito from the centre of the disc is 10 cm. Show that the friction coefficient
between the record and the mosquito is greater than 2 / 81. Take g = 10 m/s2.

Hazratganj Centre : 6,Nawal Kishore Road, Near CBI Office, Hazratganj, Lucknow 122
Gomti Nagar Centre : 4/385 Sector -4, Gomti Nagar Extension, Gomti Nagar, Lucknow
Tel : 0522-4307272, 8601281694