JEE Main Numericals: Work, Energy and Power

 Page 1


1 . A spring of spring constant 5 × 10
3
 N/m is stretched initially
by 5cm from the unstretched position. Then the work
required to stretch it further by another 5 cm is
(a) 12.50  Nm (b) 18.75  Nm
(c) 25.00  Nm (d) 6.25    Nm
2 . A particle of mass 10 g moves along a circle of radius 6.4 cm
with a constant tangential acceleration. What is the
magnitude of this acceleration if the kinetic energy of the
particle becomes equal to 8 × 10
–4
 J by the end of the second
revolution after the beginning of the motion ?
(a) 0.1 m/s
2
(b) 0.15 m/s
2
(c) 0.18 m/s
2
(d) 0.2 m/s
2
3 . A body is moved  along a straight line by a machine
delivering a constant power.  The distance moved by the
body in time ‘t’ is proportional to
( a) t
3/4
(b) t
3/2
(c) t
1/4
(d) t
1/2
4 . A ball is thrown vertically downwards from a height of 20 m
with an initial velocity v
0
. It collides with the ground and
loses 50% of its energy in collision and rebounds to the
same height. The initial velocity v
0
 is :    (Take g = 10 ms
–2
)
(a) 20 ms
–1
(b) 28 ms
–1
(c) 10 ms
–1
(d) 14 ms
–1
5 . When a rubber-band is stretched by a distance x, it exerts
restoring force of magnitude F = ax + bx
2
 where a and b are
constants. The work done in stretching the unstretched
rubber-band by L is:
( a)
23
aL bL +
(b)
( )
23
1
aL bL
2
+
(c)
23
aL bL
23
+ (d)
23
1 aL bL
223
æö
+ç÷
ç÷
èø
k r o W ,	 y g r e n E 	 d n a 	 r e w o P
J E E 	 n i a M 	 s l a c i r e m u N
Page 2


1 . A spring of spring constant 5 × 10
3
 N/m is stretched initially
by 5cm from the unstretched position. Then the work
required to stretch it further by another 5 cm is
(a) 12.50  Nm (b) 18.75  Nm
(c) 25.00  Nm (d) 6.25    Nm
2 . A particle of mass 10 g moves along a circle of radius 6.4 cm
with a constant tangential acceleration. What is the
magnitude of this acceleration if the kinetic energy of the
particle becomes equal to 8 × 10
–4
 J by the end of the second
revolution after the beginning of the motion ?
(a) 0.1 m/s
2
(b) 0.15 m/s
2
(c) 0.18 m/s
2
(d) 0.2 m/s
2
3 . A body is moved  along a straight line by a machine
delivering a constant power.  The distance moved by the
body in time ‘t’ is proportional to
( a) t
3/4
(b) t
3/2
(c) t
1/4
(d) t
1/2
4 . A ball is thrown vertically downwards from a height of 20 m
with an initial velocity v
0
. It collides with the ground and
loses 50% of its energy in collision and rebounds to the
same height. The initial velocity v
0
 is :    (Take g = 10 ms
–2
)
(a) 20 ms
–1
(b) 28 ms
–1
(c) 10 ms
–1
(d) 14 ms
–1
5 . When a rubber-band is stretched by a distance x, it exerts
restoring force of magnitude F = ax + bx
2
 where a and b are
constants. The work done in stretching the unstretched
rubber-band by L is:
( a)
23
aL bL +
(b)
( )
23
1
aL bL
2
+
(c)
23
aL bL
23
+ (d)
23
1 aL bL
223
æö
+ç÷
ç÷
èø
k r o W ,	 y g r e n E 	 d n a 	 r e w o P
J E E 	 n i a M 	 s l a c i r e m u N
6 . A particle is acted by a force F = kx, where k is a +ve constant.
Its potential energy at x = 0 is zero. Which curve correctly
represents the variation of potential energy of the block
with respect to x
( a)
U
x (b)
U
x
(c)
U
x
(d)
U
x
7 . A particle of mass m is driven by a machine that delivers a
constant power of k watts. If the particle starts from rest the
force on the particle at time t is
( a)
–1/2
mkt (b)
–1/2
2mkt
(c)
–1/2
1
mkt
2
(d)
–1/2
mk
t
2
8 . A moving body with a mass m
1
 and velocity u strikes a
stationary body of mass m
2
. The masses m
1
 and m
2
  should
be in the ratio m
1
/m
2
 so as to decrease the velocity of the
first body to 2u/3 and giving a velocity of v to m
2
 assuming
a perfectly elastic impact. Then the ratio m
1
/m
2
 is
(a) 5 (b)
5 / 1
(c)
25 / 1
(d) 25
9 . Two similar springs P and Q have spring constants K
P
 and
K
Q
, such that K
P
 > K
Q
. They are stretched, first by the same
amount (case a,) then by the same force (case b). The work
done by the springs W
P
 and W
Q
 are related as, in case (a)
and case (b), respectively
(a)W
P
 = W
Q
 ; W
P
 = W
Q
(b) W
P
 > W
Q
 ; W
Q
 > W
P
(c)W
P
 < W
Q
 ; W
Q
 < W
P
(d) W
P
 = W
Q
 ; W
P
 > W
Q
10. A body is allowed to fall freely under gravity from a height
of 10m.  If it looses 25% of its energy due to impact with the
ground, then the maximum height it rises after one impact is
(a) 2.5m (b) 5.0m (c) 7.5m (d) 8.2m
11. Water falls from a height of 60 m at the rate of 15 kg/s to
operate a turbine. The losses due to frictional force are 10%
of energy . How much power is generated by the turbine?( g
= 10 m/s
2
)
(a) 8.1 kW (b) 10.2 kW
(c) 12.3 kW (d) 7.0 kW
12. A glass marble dropped from a certain height above the
horizontal surface reaches the surface in time t and then
continues to bounce up and down. The time in which the
marble finally comes to rest is
(a)e
n
t (b) e
2
t
(c)
e
t
1e
1+éù
êú
-
ëû
(d)
ú
û
ù
ê
ë
é
+
- 1
e 1
e
t
13. A block C of mass m is moving with velocity v
0
 and collides
elastically with block A of mass m and connected to another
block B of mass 2m through spring constant k. What is k if
x
0
 is compression of spring when velocity of A and B is
same?
A B C
v
0
`
( a)
2
0
2
0
mv
x
(b)
2
0
2
0
mv
2x
(c)
2
0
2
0
mv 3
2
x
(d)
2
0
2
0
mv 2
3
x
Page 3


1 . A spring of spring constant 5 × 10
3
 N/m is stretched initially
by 5cm from the unstretched position. Then the work
required to stretch it further by another 5 cm is
(a) 12.50  Nm (b) 18.75  Nm
(c) 25.00  Nm (d) 6.25    Nm
2 . A particle of mass 10 g moves along a circle of radius 6.4 cm
with a constant tangential acceleration. What is the
magnitude of this acceleration if the kinetic energy of the
particle becomes equal to 8 × 10
–4
 J by the end of the second
revolution after the beginning of the motion ?
(a) 0.1 m/s
2
(b) 0.15 m/s
2
(c) 0.18 m/s
2
(d) 0.2 m/s
2
3 . A body is moved  along a straight line by a machine
delivering a constant power.  The distance moved by the
body in time ‘t’ is proportional to
( a) t
3/4
(b) t
3/2
(c) t
1/4
(d) t
1/2
4 . A ball is thrown vertically downwards from a height of 20 m
with an initial velocity v
0
. It collides with the ground and
loses 50% of its energy in collision and rebounds to the
same height. The initial velocity v
0
 is :    (Take g = 10 ms
–2
)
(a) 20 ms
–1
(b) 28 ms
–1
(c) 10 ms
–1
(d) 14 ms
–1
5 . When a rubber-band is stretched by a distance x, it exerts
restoring force of magnitude F = ax + bx
2
 where a and b are
constants. The work done in stretching the unstretched
rubber-band by L is:
( a)
23
aL bL +
(b)
( )
23
1
aL bL
2
+
(c)
23
aL bL
23
+ (d)
23
1 aL bL
223
æö
+ç÷
ç÷
èø
k r o W ,	 y g r e n E 	 d n a 	 r e w o P
J E E 	 n i a M 	 s l a c i r e m u N
6 . A particle is acted by a force F = kx, where k is a +ve constant.
Its potential energy at x = 0 is zero. Which curve correctly
represents the variation of potential energy of the block
with respect to x
( a)
U
x (b)
U
x
(c)
U
x
(d)
U
x
7 . A particle of mass m is driven by a machine that delivers a
constant power of k watts. If the particle starts from rest the
force on the particle at time t is
( a)
–1/2
mkt (b)
–1/2
2mkt
(c)
–1/2
1
mkt
2
(d)
–1/2
mk
t
2
8 . A moving body with a mass m
1
 and velocity u strikes a
stationary body of mass m
2
. The masses m
1
 and m
2
  should
be in the ratio m
1
/m
2
 so as to decrease the velocity of the
first body to 2u/3 and giving a velocity of v to m
2
 assuming
a perfectly elastic impact. Then the ratio m
1
/m
2
 is
(a) 5 (b)
5 / 1
(c)
25 / 1
(d) 25
9 . Two similar springs P and Q have spring constants K
P
 and
K
Q
, such that K
P
 > K
Q
. They are stretched, first by the same
amount (case a,) then by the same force (case b). The work
done by the springs W
P
 and W
Q
 are related as, in case (a)
and case (b), respectively
(a)W
P
 = W
Q
 ; W
P
 = W
Q
(b) W
P
 > W
Q
 ; W
Q
 > W
P
(c)W
P
 < W
Q
 ; W
Q
 < W
P
(d) W
P
 = W
Q
 ; W
P
 > W
Q
10. A body is allowed to fall freely under gravity from a height
of 10m.  If it looses 25% of its energy due to impact with the
ground, then the maximum height it rises after one impact is
(a) 2.5m (b) 5.0m (c) 7.5m (d) 8.2m
11. Water falls from a height of 60 m at the rate of 15 kg/s to
operate a turbine. The losses due to frictional force are 10%
of energy . How much power is generated by the turbine?( g
= 10 m/s
2
)
(a) 8.1 kW (b) 10.2 kW
(c) 12.3 kW (d) 7.0 kW
12. A glass marble dropped from a certain height above the
horizontal surface reaches the surface in time t and then
continues to bounce up and down. The time in which the
marble finally comes to rest is
(a)e
n
t (b) e
2
t
(c)
e
t
1e
1+éù
êú
-
ëû
(d)
ú
û
ù
ê
ë
é
+
- 1
e 1
e
t
13. A block C of mass m is moving with velocity v
0
 and collides
elastically with block A of mass m and connected to another
block B of mass 2m through spring constant k. What is k if
x
0
 is compression of spring when velocity of A and B is
same?
A B C
v
0
`
( a)
2
0
2
0
mv
x
(b)
2
0
2
0
mv
2x
(c)
2
0
2
0
mv 3
2
x
(d)
2
0
2
0
mv 2
3
x
14. In the figure shown, a particle of mass m is released from the
position A on a smooth track. When the particle reaches at
B, then normal reaction on it by the track is
A
B
h
3h
(a) mg (b) 2mg (c)
2
m g
3
(d)
2
mg
h
15. A body of mass 1 kg begins to move under the action of a
time dependent force 
2
ˆˆ
F (2ti 3t j)=+
r
N, where 
ˆ
i and 
ˆ
j are
unit vectors alogn x and y axis. What power will be developed
by the force at the time t?
(a) (2t
2
 + 3t
3
)W (b) (2t
2
 + 4t
4
) W
(c) (2t
3
 + 3t
4
) W (d) (2t
3
 + 3t
5
) W
16. A bullet of mass 20 g and moving with 600 m/s collides with
a block of mass 4 kg hanging with the string. What is the
velocity of bullet when it comes out of block, if block rises
to height 0.2 m after collision?
(a) 200 m/s (b) 150 m/s (c) 400 m/s (d) 300 m/s
17. A body of mass m kg is ascending on a smooth inclined
plane of inclination q
1
sin
x
æö
q=
ç÷
èø
 with constant acceleration
of a m/s
2
. The final velocity of the body is
v m/s.  The work done by the body during this motion is
(Initial velocity of the body = 0)
( a)
2
1
mv (g xa)
2
+ (b)
2
mvg
a
22
æö
+
ç÷
èø
(c) ( )
2
2mvx
a gx
a
+ (d) ( )
2
mv
g xa
2ax
+
18. The potential energy of a 1 kg particle free to move along
the x-axis is given by J
2
x
4
x
) x ( V
2 4
÷
÷
ø
ö
ç
ç
è
æ
- = .
The total mechanical energy of the particle is 2 J. Then, the
maximum speed (in m/s) is
( a)
2
3
(b)
2
(c)
2
1
(d) 2
19. A car of mass m starts from rest and accelerates so that the
instantaneous power delivered to the car has a constant
magnitude P
0
. The instantaneous velocity of this car is
proportional to :
(a)t
2
P
0
(b) t
1/2
(c)t
–1/2
(d)
t
m
20. A block of mass m rests on a rough horizontal surface
(Coefficient of friction is µ).  When a bullet of mass m/2
strikes horizontally , and get embedded in it, the block moves
a distance d before coming to rest. The initial velocity of the
bullet is k 2 gd m , then the value of k is
/////////////////////////////////////////////////////////////
m
d
m/2
(a) 2 (b) 3
(c) 4 (d) 5
21. A force acts on a 30 gm particle in such a way that the
position of the particle as a function of time is given by x =
3t – 4t
2
 + t
3
, where x is in metres and t is in seconds. The
work done during the first 4 seconds is
(a) 576 mJ (b) 450 mJ
(c) 490 mJ (d) 530 mJ
22. A steel ball of mass 5g is thrown downward with velocity 10
m/s from  height 19.5 m. It penetrates  sand by 50 cm. The
change in mechanical energy will be (g = 10 m/s
2
)
(a) 1J (b) 1.25 J
(c) 1.5 J (d) 1.75 J
Page 4


1 . A spring of spring constant 5 × 10
3
 N/m is stretched initially
by 5cm from the unstretched position. Then the work
required to stretch it further by another 5 cm is
(a) 12.50  Nm (b) 18.75  Nm
(c) 25.00  Nm (d) 6.25    Nm
2 . A particle of mass 10 g moves along a circle of radius 6.4 cm
with a constant tangential acceleration. What is the
magnitude of this acceleration if the kinetic energy of the
particle becomes equal to 8 × 10
–4
 J by the end of the second
revolution after the beginning of the motion ?
(a) 0.1 m/s
2
(b) 0.15 m/s
2
(c) 0.18 m/s
2
(d) 0.2 m/s
2
3 . A body is moved  along a straight line by a machine
delivering a constant power.  The distance moved by the
body in time ‘t’ is proportional to
( a) t
3/4
(b) t
3/2
(c) t
1/4
(d) t
1/2
4 . A ball is thrown vertically downwards from a height of 20 m
with an initial velocity v
0
. It collides with the ground and
loses 50% of its energy in collision and rebounds to the
same height. The initial velocity v
0
 is :    (Take g = 10 ms
–2
)
(a) 20 ms
–1
(b) 28 ms
–1
(c) 10 ms
–1
(d) 14 ms
–1
5 . When a rubber-band is stretched by a distance x, it exerts
restoring force of magnitude F = ax + bx
2
 where a and b are
constants. The work done in stretching the unstretched
rubber-band by L is:
( a)
23
aL bL +
(b)
( )
23
1
aL bL
2
+
(c)
23
aL bL
23
+ (d)
23
1 aL bL
223
æö
+ç÷
ç÷
èø
k r o W ,	 y g r e n E 	 d n a 	 r e w o P
J E E 	 n i a M 	 s l a c i r e m u N
6 . A particle is acted by a force F = kx, where k is a +ve constant.
Its potential energy at x = 0 is zero. Which curve correctly
represents the variation of potential energy of the block
with respect to x
( a)
U
x (b)
U
x
(c)
U
x
(d)
U
x
7 . A particle of mass m is driven by a machine that delivers a
constant power of k watts. If the particle starts from rest the
force on the particle at time t is
( a)
–1/2
mkt (b)
–1/2
2mkt
(c)
–1/2
1
mkt
2
(d)
–1/2
mk
t
2
8 . A moving body with a mass m
1
 and velocity u strikes a
stationary body of mass m
2
. The masses m
1
 and m
2
  should
be in the ratio m
1
/m
2
 so as to decrease the velocity of the
first body to 2u/3 and giving a velocity of v to m
2
 assuming
a perfectly elastic impact. Then the ratio m
1
/m
2
 is
(a) 5 (b)
5 / 1
(c)
25 / 1
(d) 25
9 . Two similar springs P and Q have spring constants K
P
 and
K
Q
, such that K
P
 > K
Q
. They are stretched, first by the same
amount (case a,) then by the same force (case b). The work
done by the springs W
P
 and W
Q
 are related as, in case (a)
and case (b), respectively
(a)W
P
 = W
Q
 ; W
P
 = W
Q
(b) W
P
 > W
Q
 ; W
Q
 > W
P
(c)W
P
 < W
Q
 ; W
Q
 < W
P
(d) W
P
 = W
Q
 ; W
P
 > W
Q
10. A body is allowed to fall freely under gravity from a height
of 10m.  If it looses 25% of its energy due to impact with the
ground, then the maximum height it rises after one impact is
(a) 2.5m (b) 5.0m (c) 7.5m (d) 8.2m
11. Water falls from a height of 60 m at the rate of 15 kg/s to
operate a turbine. The losses due to frictional force are 10%
of energy . How much power is generated by the turbine?( g
= 10 m/s
2
)
(a) 8.1 kW (b) 10.2 kW
(c) 12.3 kW (d) 7.0 kW
12. A glass marble dropped from a certain height above the
horizontal surface reaches the surface in time t and then
continues to bounce up and down. The time in which the
marble finally comes to rest is
(a)e
n
t (b) e
2
t
(c)
e
t
1e
1+éù
êú
-
ëû
(d)
ú
û
ù
ê
ë
é
+
- 1
e 1
e
t
13. A block C of mass m is moving with velocity v
0
 and collides
elastically with block A of mass m and connected to another
block B of mass 2m through spring constant k. What is k if
x
0
 is compression of spring when velocity of A and B is
same?
A B C
v
0
`
( a)
2
0
2
0
mv
x
(b)
2
0
2
0
mv
2x
(c)
2
0
2
0
mv 3
2
x
(d)
2
0
2
0
mv 2
3
x
14. In the figure shown, a particle of mass m is released from the
position A on a smooth track. When the particle reaches at
B, then normal reaction on it by the track is
A
B
h
3h
(a) mg (b) 2mg (c)
2
m g
3
(d)
2
mg
h
15. A body of mass 1 kg begins to move under the action of a
time dependent force 
2
ˆˆ
F (2ti 3t j)=+
r
N, where 
ˆ
i and 
ˆ
j are
unit vectors alogn x and y axis. What power will be developed
by the force at the time t?
(a) (2t
2
 + 3t
3
)W (b) (2t
2
 + 4t
4
) W
(c) (2t
3
 + 3t
4
) W (d) (2t
3
 + 3t
5
) W
16. A bullet of mass 20 g and moving with 600 m/s collides with
a block of mass 4 kg hanging with the string. What is the
velocity of bullet when it comes out of block, if block rises
to height 0.2 m after collision?
(a) 200 m/s (b) 150 m/s (c) 400 m/s (d) 300 m/s
17. A body of mass m kg is ascending on a smooth inclined
plane of inclination q
1
sin
x
æö
q=
ç÷
èø
 with constant acceleration
of a m/s
2
. The final velocity of the body is
v m/s.  The work done by the body during this motion is
(Initial velocity of the body = 0)
( a)
2
1
mv (g xa)
2
+ (b)
2
mvg
a
22
æö
+
ç÷
èø
(c) ( )
2
2mvx
a gx
a
+ (d) ( )
2
mv
g xa
2ax
+
18. The potential energy of a 1 kg particle free to move along
the x-axis is given by J
2
x
4
x
) x ( V
2 4
÷
÷
ø
ö
ç
ç
è
æ
- = .
The total mechanical energy of the particle is 2 J. Then, the
maximum speed (in m/s) is
( a)
2
3
(b)
2
(c)
2
1
(d) 2
19. A car of mass m starts from rest and accelerates so that the
instantaneous power delivered to the car has a constant
magnitude P
0
. The instantaneous velocity of this car is
proportional to :
(a)t
2
P
0
(b) t
1/2
(c)t
–1/2
(d)
t
m
20. A block of mass m rests on a rough horizontal surface
(Coefficient of friction is µ).  When a bullet of mass m/2
strikes horizontally , and get embedded in it, the block moves
a distance d before coming to rest. The initial velocity of the
bullet is k 2 gd m , then the value of k is
/////////////////////////////////////////////////////////////
m
d
m/2
(a) 2 (b) 3
(c) 4 (d) 5
21. A force acts on a 30 gm particle in such a way that the
position of the particle as a function of time is given by x =
3t – 4t
2
 + t
3
, where x is in metres and t is in seconds. The
work done during the first 4 seconds is
(a) 576 mJ (b) 450 mJ
(c) 490 mJ (d) 530 mJ
22. A steel ball of mass 5g is thrown downward with velocity 10
m/s from  height 19.5 m. It penetrates  sand by 50 cm. The
change in mechanical energy will be (g = 10 m/s
2
)
(a) 1J (b) 1.25 J
(c) 1.5 J (d) 1.75 J
   
23. A 10 H.P . motor pumps out water from a well of depth 20 m
and fills a water tank of volume 22380 litres at a height of
10 m from the ground. The running time of the motor to fill
the empty water tank is (g = 10ms
–2
)
(a) 5 minutes (b) 10 minutes
(c) 15 minutes (d) 20 minutes
24. A 3 kg ball stri kes a heavy ri gid wall w ith a speed
of 10 m/s at an angle of 60º. It gets reflected with
the same speed and angle as shown here. If the
ball is in contact with the wall for 0.20s, what is
the average force exerted on the ball by the wall?
60º
60º
(a) 150 N (b) 300 N (c)
N 3 150
(d) zero
25. A 2 kg block slides on a horizontal floor with a speed of 4m/s.
It strikes a uncompressed spring, and compresses it till the
block is motionless. The kinetic friction force is 15N and spring
constant is 10,000 N/m. The spring compresses by
(a) 8.5 cm (b) 5.5 cm (c) 2.5 cm (d) 11.0 cm
26. A stone is tied to a string of length l and is whirled in a
vertical circle with the other end of the string as the centre.
At a certain instant of time, the stone is at its lowest position
and has a speed u. The magnitude of the change in velocity
as it reaches a position where the string is horizontal
 (g being acceleration due to gravity) is
( a) l g 2 (b)
) g u ( 2
2
l -
(c) l g u
2
- (d) l g 2 u u
2
- -
27. An engine pumps water through a hose pipe. Water passes
through the pipe and leaves it with a velocity of 2 m/s. The
mass per unit length of water in the pipe is 100 kg/m. What
is the power of the engine?
(a) 400 W (b) 200 W
(c) 100 W (d) 800 W
28. A body of mass 50kg is projected vertically upwards with
velocity of 100 m/sec. After 5 seconds this body breaks into
two pieces of 20 kg and 30 kg. If 20 kg piece travels upwards
with 150 m/sec, then the velocity of other block will be
(a) 15 m/sec downwards (b) 15 m/sec upwards
(c) 51 m/sec downwards (d) 51 m/sec upwards
29. The K.E. acquired by a mass m in travelling a certain distance
d, starting form rest, under the action of a constant force is
directly proportional to
(a) m (b)
m
(c)
m
1
(d) independent of m
30. A vertical spring with force constant k is fixed on a table. A
ball of mass m at a height h above the free upper end of the
spring falls vertically on the spring so that the spring is
compressed by a distance d. The net work done in the
process is
( a)
2
1
mg(h d) kd
2
+- (b)
2
1
mg(h d) kd
2
--
(c)
2
1
mg(h d) kd
2
-+ (d)
2
1
mg(h d) kd
2
++
  
Page 5


1 . A spring of spring constant 5 × 10
3
 N/m is stretched initially
by 5cm from the unstretched position. Then the work
required to stretch it further by another 5 cm is
(a) 12.50  Nm (b) 18.75  Nm
(c) 25.00  Nm (d) 6.25    Nm
2 . A particle of mass 10 g moves along a circle of radius 6.4 cm
with a constant tangential acceleration. What is the
magnitude of this acceleration if the kinetic energy of the
particle becomes equal to 8 × 10
–4
 J by the end of the second
revolution after the beginning of the motion ?
(a) 0.1 m/s
2
(b) 0.15 m/s
2
(c) 0.18 m/s
2
(d) 0.2 m/s
2
3 . A body is moved  along a straight line by a machine
delivering a constant power.  The distance moved by the
body in time ‘t’ is proportional to
( a) t
3/4
(b) t
3/2
(c) t
1/4
(d) t
1/2
4 . A ball is thrown vertically downwards from a height of 20 m
with an initial velocity v
0
. It collides with the ground and
loses 50% of its energy in collision and rebounds to the
same height. The initial velocity v
0
 is :    (Take g = 10 ms
–2
)
(a) 20 ms
–1
(b) 28 ms
–1
(c) 10 ms
–1
(d) 14 ms
–1
5 . When a rubber-band is stretched by a distance x, it exerts
restoring force of magnitude F = ax + bx
2
 where a and b are
constants. The work done in stretching the unstretched
rubber-band by L is:
( a)
23
aL bL +
(b)
( )
23
1
aL bL
2
+
(c)
23
aL bL
23
+ (d)
23
1 aL bL
223
æö
+ç÷
ç÷
èø
k r o W ,	 y g r e n E 	 d n a 	 r e w o P
J E E 	 n i a M 	 s l a c i r e m u N
6 . A particle is acted by a force F = kx, where k is a +ve constant.
Its potential energy at x = 0 is zero. Which curve correctly
represents the variation of potential energy of the block
with respect to x
( a)
U
x (b)
U
x
(c)
U
x
(d)
U
x
7 . A particle of mass m is driven by a machine that delivers a
constant power of k watts. If the particle starts from rest the
force on the particle at time t is
( a)
–1/2
mkt (b)
–1/2
2mkt
(c)
–1/2
1
mkt
2
(d)
–1/2
mk
t
2
8 . A moving body with a mass m
1
 and velocity u strikes a
stationary body of mass m
2
. The masses m
1
 and m
2
  should
be in the ratio m
1
/m
2
 so as to decrease the velocity of the
first body to 2u/3 and giving a velocity of v to m
2
 assuming
a perfectly elastic impact. Then the ratio m
1
/m
2
 is
(a) 5 (b)
5 / 1
(c)
25 / 1
(d) 25
9 . Two similar springs P and Q have spring constants K
P
 and
K
Q
, such that K
P
 > K
Q
. They are stretched, first by the same
amount (case a,) then by the same force (case b). The work
done by the springs W
P
 and W
Q
 are related as, in case (a)
and case (b), respectively
(a)W
P
 = W
Q
 ; W
P
 = W
Q
(b) W
P
 > W
Q
 ; W
Q
 > W
P
(c)W
P
 < W
Q
 ; W
Q
 < W
P
(d) W
P
 = W
Q
 ; W
P
 > W
Q
10. A body is allowed to fall freely under gravity from a height
of 10m.  If it looses 25% of its energy due to impact with the
ground, then the maximum height it rises after one impact is
(a) 2.5m (b) 5.0m (c) 7.5m (d) 8.2m
11. Water falls from a height of 60 m at the rate of 15 kg/s to
operate a turbine. The losses due to frictional force are 10%
of energy . How much power is generated by the turbine?( g
= 10 m/s
2
)
(a) 8.1 kW (b) 10.2 kW
(c) 12.3 kW (d) 7.0 kW
12. A glass marble dropped from a certain height above the
horizontal surface reaches the surface in time t and then
continues to bounce up and down. The time in which the
marble finally comes to rest is
(a)e
n
t (b) e
2
t
(c)
e
t
1e
1+éù
êú
-
ëû
(d)
ú
û
ù
ê
ë
é
+
- 1
e 1
e
t
13. A block C of mass m is moving with velocity v
0
 and collides
elastically with block A of mass m and connected to another
block B of mass 2m through spring constant k. What is k if
x
0
 is compression of spring when velocity of A and B is
same?
A B C
v
0
`
( a)
2
0
2
0
mv
x
(b)
2
0
2
0
mv
2x
(c)
2
0
2
0
mv 3
2
x
(d)
2
0
2
0
mv 2
3
x
14. In the figure shown, a particle of mass m is released from the
position A on a smooth track. When the particle reaches at
B, then normal reaction on it by the track is
A
B
h
3h
(a) mg (b) 2mg (c)
2
m g
3
(d)
2
mg
h
15. A body of mass 1 kg begins to move under the action of a
time dependent force 
2
ˆˆ
F (2ti 3t j)=+
r
N, where 
ˆ
i and 
ˆ
j are
unit vectors alogn x and y axis. What power will be developed
by the force at the time t?
(a) (2t
2
 + 3t
3
)W (b) (2t
2
 + 4t
4
) W
(c) (2t
3
 + 3t
4
) W (d) (2t
3
 + 3t
5
) W
16. A bullet of mass 20 g and moving with 600 m/s collides with
a block of mass 4 kg hanging with the string. What is the
velocity of bullet when it comes out of block, if block rises
to height 0.2 m after collision?
(a) 200 m/s (b) 150 m/s (c) 400 m/s (d) 300 m/s
17. A body of mass m kg is ascending on a smooth inclined
plane of inclination q
1
sin
x
æö
q=
ç÷
èø
 with constant acceleration
of a m/s
2
. The final velocity of the body is
v m/s.  The work done by the body during this motion is
(Initial velocity of the body = 0)
( a)
2
1
mv (g xa)
2
+ (b)
2
mvg
a
22
æö
+
ç÷
èø
(c) ( )
2
2mvx
a gx
a
+ (d) ( )
2
mv
g xa
2ax
+
18. The potential energy of a 1 kg particle free to move along
the x-axis is given by J
2
x
4
x
) x ( V
2 4
÷
÷
ø
ö
ç
ç
è
æ
- = .
The total mechanical energy of the particle is 2 J. Then, the
maximum speed (in m/s) is
( a)
2
3
(b)
2
(c)
2
1
(d) 2
19. A car of mass m starts from rest and accelerates so that the
instantaneous power delivered to the car has a constant
magnitude P
0
. The instantaneous velocity of this car is
proportional to :
(a)t
2
P
0
(b) t
1/2
(c)t
–1/2
(d)
t
m
20. A block of mass m rests on a rough horizontal surface
(Coefficient of friction is µ).  When a bullet of mass m/2
strikes horizontally , and get embedded in it, the block moves
a distance d before coming to rest. The initial velocity of the
bullet is k 2 gd m , then the value of k is
/////////////////////////////////////////////////////////////
m
d
m/2
(a) 2 (b) 3
(c) 4 (d) 5
21. A force acts on a 30 gm particle in such a way that the
position of the particle as a function of time is given by x =
3t – 4t
2
 + t
3
, where x is in metres and t is in seconds. The
work done during the first 4 seconds is
(a) 576 mJ (b) 450 mJ
(c) 490 mJ (d) 530 mJ
22. A steel ball of mass 5g is thrown downward with velocity 10
m/s from  height 19.5 m. It penetrates  sand by 50 cm. The
change in mechanical energy will be (g = 10 m/s
2
)
(a) 1J (b) 1.25 J
(c) 1.5 J (d) 1.75 J
   
23. A 10 H.P . motor pumps out water from a well of depth 20 m
and fills a water tank of volume 22380 litres at a height of
10 m from the ground. The running time of the motor to fill
the empty water tank is (g = 10ms
–2
)
(a) 5 minutes (b) 10 minutes
(c) 15 minutes (d) 20 minutes
24. A 3 kg ball stri kes a heavy ri gid wall w ith a speed
of 10 m/s at an angle of 60º. It gets reflected with
the same speed and angle as shown here. If the
ball is in contact with the wall for 0.20s, what is
the average force exerted on the ball by the wall?
60º
60º
(a) 150 N (b) 300 N (c)
N 3 150
(d) zero
25. A 2 kg block slides on a horizontal floor with a speed of 4m/s.
It strikes a uncompressed spring, and compresses it till the
block is motionless. The kinetic friction force is 15N and spring
constant is 10,000 N/m. The spring compresses by
(a) 8.5 cm (b) 5.5 cm (c) 2.5 cm (d) 11.0 cm
26. A stone is tied to a string of length l and is whirled in a
vertical circle with the other end of the string as the centre.
At a certain instant of time, the stone is at its lowest position
and has a speed u. The magnitude of the change in velocity
as it reaches a position where the string is horizontal
 (g being acceleration due to gravity) is
( a) l g 2 (b)
) g u ( 2
2
l -
(c) l g u
2
- (d) l g 2 u u
2
- -
27. An engine pumps water through a hose pipe. Water passes
through the pipe and leaves it with a velocity of 2 m/s. The
mass per unit length of water in the pipe is 100 kg/m. What
is the power of the engine?
(a) 400 W (b) 200 W
(c) 100 W (d) 800 W
28. A body of mass 50kg is projected vertically upwards with
velocity of 100 m/sec. After 5 seconds this body breaks into
two pieces of 20 kg and 30 kg. If 20 kg piece travels upwards
with 150 m/sec, then the velocity of other block will be
(a) 15 m/sec downwards (b) 15 m/sec upwards
(c) 51 m/sec downwards (d) 51 m/sec upwards
29. The K.E. acquired by a mass m in travelling a certain distance
d, starting form rest, under the action of a constant force is
directly proportional to
(a) m (b)
m
(c)
m
1
(d) independent of m
30. A vertical spring with force constant k is fixed on a table. A
ball of mass m at a height h above the free upper end of the
spring falls vertically on the spring so that the spring is
compressed by a distance d. The net work done in the
process is
( a)
2
1
mg(h d) kd
2
+- (b)
2
1
mg(h d) kd
2
--
(c)
2
1
mg(h d) kd
2
-+ (d)
2
1
mg(h d) kd
2
++
  
1. (b) k = 5 × 10
3
 N/m
( )
22
21
1
2
Wkxx=- 
322
1
5 10 (0.1) (0.05)
2
éù
=´´-
ëû
5000
0.15 0.05 18.75 Nm
2
=´´=
2 . ( a ) Given: Mass of particle, M = 10g = 
10
kg
1000
radius of circle R = 6.4 cm
Kinetic energy E of particle = 8 × 10
–4
J
acceleration a
t
 = ?
2
1
mv
2
 = E
Þ
2
1 10
v
2 1000
æö
ç÷
èø
 = 8 × 10
–4
Þ v
2
 = 16 × 10
–2
Þ v = 4 × 10
–1
 = 0.4 m/s
Now, using
v
2
 = u
2
 + 2a
t
s (s = 4pR)
(0.4)
2
 = 0
2
 + 2a
t
 
22 6.4
4
7 100
æö
´´
ç÷
èø
Þa
t
 = (0.4)
2
 × 
7 100
8 22 6.4
´
´´
 = 0.1 m/s
2
3. (b) We know that  F × v = Power
Fvc \´=   where c = constant
dv mdv
m v c F ma
dt dt
æö
´===
ç÷
èø
Q
00
vt
m vdv c dt=
òò
2
1
2
mv ctÞ=
1
2
2c
vt
m
=´
1
2
2
where
dx c dx
tv
dt m dt
=´=
1
2
00
2
xt
c
dx t dt
m
=´
òò
3
2
22
3
ct
x
m
=´  
3
2
xtÞµ
4. (a) When ball collides with the ground it loses its 50% of
energy
\ 
f
i
K E 1
KE2
=
Þ  
2
f
2
1
mV
1
2
1
2
2
=
or 
f
i
V 1
V 2
=
or, 
2
0
2gh 1
2
v 2gh
=
+
or, 4gh = 
2
0
v 2gh +
\ v
0
 = 20ms
–1
M
M
5. (c) Work done in stretching the rubber-band by a distance
dx is
dW = F dx = (ax + bx
2
)dx
Integrating both sides,
23
2
00
23
=+=+
òò
LL
aL bL
W axdx bx dx
6. (b) We know that DU = – W for conservative forces
DU = 
0
x
Fdx -
ò
 or DU = 
0
x
k xdx -
ò
Þ U
(x)
 – U
(0)
 = 
2
2
kx
-
Given     U
(0)
 = 0
      U
(x)
 = 
2
2
kx
-
This is the equation of a parabola, which is symmetric
to U-axis in negative direction.
7. (d) As we know power P = 
dw
dt
Þ w = Pt = 
1
2
 mv
2
So, v = 
2Pt
m
Hence, acceleration 
dv2P1
a.
dtm2t
==
Therefore, force on the particle at time ‘t’
= ma = 
2
–1/2
2Km 1 Km mK
.t
2t2 2t
==
HINTS & SOLUTIONS