JEE Main Numericals: Laws of Motion | Physics for JEE Main & Advanced PDF Download

 Page 1


1 . A player stops a football weighing 0.5 kg which comes flying
towards him with a velocity of 10m/s. If the impact lasts for
1/50th sec. and the ball bounces back with a velocity of 15
m/s, then the average force involved is
(a) 250 N (b) 1250 N
(c) 500 N (d) 625 N
2 . A 5000 kg rocket is set for vertical firing. The exhaust speed
is 800 m/s. To give an initial upward acceleration of 20 m/s
2
,
the amount of gas ejected per second to supply the needed
thrust will be (Take g = 10 m/s
2
)
(a) 127.5 kg/s (b) 137.5 kg/s
(c) 155.5 kg/s (d) 187.5 kg/s
3 . A mass ‘m’ is supported by a massless string wound around
a uniform hollow cylinder of mass m and radius R. If the
string does not slip on the cylinder, with what acceleration
will the mass release?
( a)
2g
3
(b)
g
2
m
R
m
(c)
5g
6
(d) g
s w a L 	 f o 	 n o i t o M
J E E 	 n i a M 	 s l a c i r e m u N
Page 2


1 . A player stops a football weighing 0.5 kg which comes flying
towards him with a velocity of 10m/s. If the impact lasts for
1/50th sec. and the ball bounces back with a velocity of 15
m/s, then the average force involved is
(a) 250 N (b) 1250 N
(c) 500 N (d) 625 N
2 . A 5000 kg rocket is set for vertical firing. The exhaust speed
is 800 m/s. To give an initial upward acceleration of 20 m/s
2
,
the amount of gas ejected per second to supply the needed
thrust will be (Take g = 10 m/s
2
)
(a) 127.5 kg/s (b) 137.5 kg/s
(c) 155.5 kg/s (d) 187.5 kg/s
3 . A mass ‘m’ is supported by a massless string wound around
a uniform hollow cylinder of mass m and radius R. If the
string does not slip on the cylinder, with what acceleration
will the mass release?
( a)
2g
3
(b)
g
2
m
R
m
(c)
5g
6
(d) g
s w a L 	 f o 	 n o i t o M
J E E 	 n i a M 	 s l a c i r e m u N
4 . A 40 kg slab rests on a frictionless floor as shown in
the figure. A 10 kg block rests on the top of the slab. The
static coefficient of friction between the block and slab
is 0.60 while the coefficient of kinetic friction is 0.40. The
10 kg block is acted upon by a horizontal force of 100 N. If
g = 9.8 m/s
2
, the resultaing acceleration of the slab will be
40 kg
10 kg
B
A
100 N
(a) 0.98 m/s
2
(b) 1.47 m/s
2
(c) 1.52 m/s
2
(d) 6.1 m/s
2
5 . The pulleys and strings shown in the figure are smooth and
of negligible mass. For the system to remain in equilibrium,
the angle q should be
 
q 
m m 
Ö 2 m  
(a)0
o
(b) 30
o
(c) 45
o
(d) 60
o
6 . A satellite in a force free space sweeps stationary
interplanetary dust at a rate (dM/dt) = av. The acceleration
of satellite is
( a)
2
2v
M
-a
(b)
2
v
M
-a
(c)
2
v
2M
-a
(d) – av
2
7 . A monkey is decending from the branch of a tree with
constant acceleration. If the breaking strength is 75% of the
weight of the monkey , the minimum acceleration with which
monkey can slide down without breaking the branch is
(a) g (b)
4
g 3
(c)
4
g
(d)
2
g
mg
q
8 . A plank with a box on it at one end
is gradually raised about the other
end. As the angle of inclination with
the horizontal reaches 30º the box
starts to slip and slides 4.0 m down
the plank in 4.0s. The coefficients of static and kinetic friction
between the box and the plank will be, respectively :
(a) 0.6 and 0.5 (b) 0.5 and 0.6
(c) 0.4 and 0.3 (d) 0.6 and 0.6
9 . A car having a mass of 1000 kg is moving at a speed of 30
metres/sec. Brakes are applied to bring the car to rest. If the
frictional force between the tyres and the road surface is
5000 newtons, the car will come to rest in
(a) 5 seconds (b) 10 seconds
(c) 12 seconds (d) 6 seconds
45° 45°
m 2m
A B
10. Block A of mass m and block B of
mass 2m are placed on a fixed
triangular wedge by means of a
massless, inextensible string and a
frictionless pulley as shown in figure.
The wedge is inclined at 45° to the horizontal on both the
sides. If the coefficient of friction between the block A and
the wedge is 2/3 and that between the block B and the wedge
is 1/3 and both the blocks A and B are released from rest, the
acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
11. The rate of mass of the gas emitted from rear of a rocket is
initially 0.1 kg/sec. If the speed of the gas relative to the
rocket is 50 m/sec and mass of the rocket is 2 kg, then the
acceleration of the rocket in m/sec
2 
is
(a) 5 (b) 5.2 (c) 2.5 (d) 25
12. A block of mass m is resting on a smooth horizontal surface.
One end of a uniform rope of mass (m/3) is fixed to the block,
which is pulled in the horizontal direction by applying a
force F at the other end. The tension in the middle of the
rope is
( a)
8
F
7
(b)
1
F
7
(c)
1
F
8
(d)
7
F
8
13. A body of mass M is kept on a rough horizontal surface
(friction coefficient µ). A person is trying to pull the body
by applying a horizontal force but the body is not moving.
The force by the surface on the body is F, then
(a) F = Mg
(b) F = mMg
(c)
2
Mg F Mg 1 µ££+
(d)
2
Mg F Mg 1 µ³³+
Page 3


1 . A player stops a football weighing 0.5 kg which comes flying
towards him with a velocity of 10m/s. If the impact lasts for
1/50th sec. and the ball bounces back with a velocity of 15
m/s, then the average force involved is
(a) 250 N (b) 1250 N
(c) 500 N (d) 625 N
2 . A 5000 kg rocket is set for vertical firing. The exhaust speed
is 800 m/s. To give an initial upward acceleration of 20 m/s
2
,
the amount of gas ejected per second to supply the needed
thrust will be (Take g = 10 m/s
2
)
(a) 127.5 kg/s (b) 137.5 kg/s
(c) 155.5 kg/s (d) 187.5 kg/s
3 . A mass ‘m’ is supported by a massless string wound around
a uniform hollow cylinder of mass m and radius R. If the
string does not slip on the cylinder, with what acceleration
will the mass release?
( a)
2g
3
(b)
g
2
m
R
m
(c)
5g
6
(d) g
s w a L 	 f o 	 n o i t o M
J E E 	 n i a M 	 s l a c i r e m u N
4 . A 40 kg slab rests on a frictionless floor as shown in
the figure. A 10 kg block rests on the top of the slab. The
static coefficient of friction between the block and slab
is 0.60 while the coefficient of kinetic friction is 0.40. The
10 kg block is acted upon by a horizontal force of 100 N. If
g = 9.8 m/s
2
, the resultaing acceleration of the slab will be
40 kg
10 kg
B
A
100 N
(a) 0.98 m/s
2
(b) 1.47 m/s
2
(c) 1.52 m/s
2
(d) 6.1 m/s
2
5 . The pulleys and strings shown in the figure are smooth and
of negligible mass. For the system to remain in equilibrium,
the angle q should be
 
q 
m m 
Ö 2 m  
(a)0
o
(b) 30
o
(c) 45
o
(d) 60
o
6 . A satellite in a force free space sweeps stationary
interplanetary dust at a rate (dM/dt) = av. The acceleration
of satellite is
( a)
2
2v
M
-a
(b)
2
v
M
-a
(c)
2
v
2M
-a
(d) – av
2
7 . A monkey is decending from the branch of a tree with
constant acceleration. If the breaking strength is 75% of the
weight of the monkey , the minimum acceleration with which
monkey can slide down without breaking the branch is
(a) g (b)
4
g 3
(c)
4
g
(d)
2
g
mg
q
8 . A plank with a box on it at one end
is gradually raised about the other
end. As the angle of inclination with
the horizontal reaches 30º the box
starts to slip and slides 4.0 m down
the plank in 4.0s. The coefficients of static and kinetic friction
between the box and the plank will be, respectively :
(a) 0.6 and 0.5 (b) 0.5 and 0.6
(c) 0.4 and 0.3 (d) 0.6 and 0.6
9 . A car having a mass of 1000 kg is moving at a speed of 30
metres/sec. Brakes are applied to bring the car to rest. If the
frictional force between the tyres and the road surface is
5000 newtons, the car will come to rest in
(a) 5 seconds (b) 10 seconds
(c) 12 seconds (d) 6 seconds
45° 45°
m 2m
A B
10. Block A of mass m and block B of
mass 2m are placed on a fixed
triangular wedge by means of a
massless, inextensible string and a
frictionless pulley as shown in figure.
The wedge is inclined at 45° to the horizontal on both the
sides. If the coefficient of friction between the block A and
the wedge is 2/3 and that between the block B and the wedge
is 1/3 and both the blocks A and B are released from rest, the
acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
11. The rate of mass of the gas emitted from rear of a rocket is
initially 0.1 kg/sec. If the speed of the gas relative to the
rocket is 50 m/sec and mass of the rocket is 2 kg, then the
acceleration of the rocket in m/sec
2 
is
(a) 5 (b) 5.2 (c) 2.5 (d) 25
12. A block of mass m is resting on a smooth horizontal surface.
One end of a uniform rope of mass (m/3) is fixed to the block,
which is pulled in the horizontal direction by applying a
force F at the other end. The tension in the middle of the
rope is
( a)
8
F
7
(b)
1
F
7
(c)
1
F
8
(d)
7
F
8
13. A body of mass M is kept on a rough horizontal surface
(friction coefficient µ). A person is trying to pull the body
by applying a horizontal force but the body is not moving.
The force by the surface on the body is F, then
(a) F = Mg
(b) F = mMg
(c)
2
Mg F Mg 1 µ££+
(d)
2
Mg F Mg 1 µ³³+
14. Which one of the following motions on a smooth plane
surface does not involve force?
(a) Accelerated motion in a straight line
(b) Retarded motion in a straight line
(c) Motion with constant momentum along a straight line
(d) Motion along a straight line with varying velocity
15. A block A of mass m
1
 rests on a horizontal table. A light
string connected to it passes over a frictionless pulley at
the edge of table and from its other end another block B of
mass m
2
 is suspended. The coefficient of kinetic friction
between the block and the table is µ
k
. When the block A is
sliding on the table, the tension in the string is
( a)
2k1
12
(m – m)g
(mm)
m
+
(b)
12k
12
mm(1 )g
(mm)
+m
+
(c)
12k
12
mm(1– )g
(mm)
m
+
(d)
2k1
12
(m m)g
(mm)
+m
+
16. The upper half of an inclined plane with inclination f is perfectly
smooth while the lower half is rough. A body starting from rest
at the top will again come to rest at the bottom if the coefficient
of friction for the lower half is given by
(a) 2 cos f (b) 2 sin f (c) tan f (d) 2 tan f
17. A particle describes a horizontal circle in a conical funnel
whose inner surface is smooth with speed of 0.5 m/s. What
is the height of the plane of circle from vertex of the funnel?
(a) 0.25 cm (b) 2 cm (c) 4 cm (d) 2.5 cm
18. Two particles of mass m each are
tied at the ends of a light string of
length 2a. The whole system is
kept on a frictionless horizontal
surface with the string held tight
so that each mass is at a distance
'a' from the centre P (as shown in
the figure).
m m
a a
P
F
Now , the mid-point of the string is pulled vertically upwards
with a small but constant force F. As a result, the particles move
towards each other on the surface. The magnitude of
acceleration, when the separation between them becomes 2x, is
( a)
22 2
Fa
m
ax -
(b)
22 2
Fx
m
ax -
(c)
2
Fx
ma
(d)
22
2
Fax
mx
-
A
B
30º
19. Two blocks are connected over a
massless pulley as shown in fig.
The mass of block A is 10 kg and
the coefficient of kinetic friction is
0.2. Block A slides down the incline
at constant speed. The mass of
block B in kg is
(a) 3.5 (b) 3.3 (c) 3.0 (d) 2.5
20. A light spring balance hangs from the hook of the other
light spring balance and a block of mass M kg hangs from
the former one. Then the true statement about the scale
reading is
(a) both the scales read M kg each
(b) the scale of the lower one reads M kg and of the upper
one zero
(c) the reading of the two scales can be anything but the
sum of the reading will be M kg
(d) both the scales read M/2 kg each
21. Tension in the cable supporting an elevator, is equal to the
weight of the elevator. From this, we can conclude that the
elevator is going up or down with a
(a) uniform velocity (b) uniform acceleration
(c) variable acceleration (d) either (b) or (c)
22. A particle tied to a string describes a vertical circular motion
of radius r continually. If it has a velocity 3gr at the
highest point, then the ratio of the respective tensions in
the string holding it at the highest and lowest points is
(a) 4 : 3 (b) 5 : 4 (c) 1 : 4 (d) 3 : 2
23. A block of mass m is connected to another block of mass M
by  a spring (massless) of spring constant k. The block are
kept on a smooth horizontal plane. Initially the blocks are at
rest and the spring is unstretched. Then a constant force F
starts acting on the block of mass M to pull it. Find the force
of the block of mass m.
( a)
() +
MF
mM
(b)
mF
M
(c)
() +MmF
m
(d)
() +
mF
mM
Page 4


1 . A player stops a football weighing 0.5 kg which comes flying
towards him with a velocity of 10m/s. If the impact lasts for
1/50th sec. and the ball bounces back with a velocity of 15
m/s, then the average force involved is
(a) 250 N (b) 1250 N
(c) 500 N (d) 625 N
2 . A 5000 kg rocket is set for vertical firing. The exhaust speed
is 800 m/s. To give an initial upward acceleration of 20 m/s
2
,
the amount of gas ejected per second to supply the needed
thrust will be (Take g = 10 m/s
2
)
(a) 127.5 kg/s (b) 137.5 kg/s
(c) 155.5 kg/s (d) 187.5 kg/s
3 . A mass ‘m’ is supported by a massless string wound around
a uniform hollow cylinder of mass m and radius R. If the
string does not slip on the cylinder, with what acceleration
will the mass release?
( a)
2g
3
(b)
g
2
m
R
m
(c)
5g
6
(d) g
s w a L 	 f o 	 n o i t o M
J E E 	 n i a M 	 s l a c i r e m u N
4 . A 40 kg slab rests on a frictionless floor as shown in
the figure. A 10 kg block rests on the top of the slab. The
static coefficient of friction between the block and slab
is 0.60 while the coefficient of kinetic friction is 0.40. The
10 kg block is acted upon by a horizontal force of 100 N. If
g = 9.8 m/s
2
, the resultaing acceleration of the slab will be
40 kg
10 kg
B
A
100 N
(a) 0.98 m/s
2
(b) 1.47 m/s
2
(c) 1.52 m/s
2
(d) 6.1 m/s
2
5 . The pulleys and strings shown in the figure are smooth and
of negligible mass. For the system to remain in equilibrium,
the angle q should be
 
q 
m m 
Ö 2 m  
(a)0
o
(b) 30
o
(c) 45
o
(d) 60
o
6 . A satellite in a force free space sweeps stationary
interplanetary dust at a rate (dM/dt) = av. The acceleration
of satellite is
( a)
2
2v
M
-a
(b)
2
v
M
-a
(c)
2
v
2M
-a
(d) – av
2
7 . A monkey is decending from the branch of a tree with
constant acceleration. If the breaking strength is 75% of the
weight of the monkey , the minimum acceleration with which
monkey can slide down without breaking the branch is
(a) g (b)
4
g 3
(c)
4
g
(d)
2
g
mg
q
8 . A plank with a box on it at one end
is gradually raised about the other
end. As the angle of inclination with
the horizontal reaches 30º the box
starts to slip and slides 4.0 m down
the plank in 4.0s. The coefficients of static and kinetic friction
between the box and the plank will be, respectively :
(a) 0.6 and 0.5 (b) 0.5 and 0.6
(c) 0.4 and 0.3 (d) 0.6 and 0.6
9 . A car having a mass of 1000 kg is moving at a speed of 30
metres/sec. Brakes are applied to bring the car to rest. If the
frictional force between the tyres and the road surface is
5000 newtons, the car will come to rest in
(a) 5 seconds (b) 10 seconds
(c) 12 seconds (d) 6 seconds
45° 45°
m 2m
A B
10. Block A of mass m and block B of
mass 2m are placed on a fixed
triangular wedge by means of a
massless, inextensible string and a
frictionless pulley as shown in figure.
The wedge is inclined at 45° to the horizontal on both the
sides. If the coefficient of friction between the block A and
the wedge is 2/3 and that between the block B and the wedge
is 1/3 and both the blocks A and B are released from rest, the
acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
11. The rate of mass of the gas emitted from rear of a rocket is
initially 0.1 kg/sec. If the speed of the gas relative to the
rocket is 50 m/sec and mass of the rocket is 2 kg, then the
acceleration of the rocket in m/sec
2 
is
(a) 5 (b) 5.2 (c) 2.5 (d) 25
12. A block of mass m is resting on a smooth horizontal surface.
One end of a uniform rope of mass (m/3) is fixed to the block,
which is pulled in the horizontal direction by applying a
force F at the other end. The tension in the middle of the
rope is
( a)
8
F
7
(b)
1
F
7
(c)
1
F
8
(d)
7
F
8
13. A body of mass M is kept on a rough horizontal surface
(friction coefficient µ). A person is trying to pull the body
by applying a horizontal force but the body is not moving.
The force by the surface on the body is F, then
(a) F = Mg
(b) F = mMg
(c)
2
Mg F Mg 1 µ££+
(d)
2
Mg F Mg 1 µ³³+
14. Which one of the following motions on a smooth plane
surface does not involve force?
(a) Accelerated motion in a straight line
(b) Retarded motion in a straight line
(c) Motion with constant momentum along a straight line
(d) Motion along a straight line with varying velocity
15. A block A of mass m
1
 rests on a horizontal table. A light
string connected to it passes over a frictionless pulley at
the edge of table and from its other end another block B of
mass m
2
 is suspended. The coefficient of kinetic friction
between the block and the table is µ
k
. When the block A is
sliding on the table, the tension in the string is
( a)
2k1
12
(m – m)g
(mm)
m
+
(b)
12k
12
mm(1 )g
(mm)
+m
+
(c)
12k
12
mm(1– )g
(mm)
m
+
(d)
2k1
12
(m m)g
(mm)
+m
+
16. The upper half of an inclined plane with inclination f is perfectly
smooth while the lower half is rough. A body starting from rest
at the top will again come to rest at the bottom if the coefficient
of friction for the lower half is given by
(a) 2 cos f (b) 2 sin f (c) tan f (d) 2 tan f
17. A particle describes a horizontal circle in a conical funnel
whose inner surface is smooth with speed of 0.5 m/s. What
is the height of the plane of circle from vertex of the funnel?
(a) 0.25 cm (b) 2 cm (c) 4 cm (d) 2.5 cm
18. Two particles of mass m each are
tied at the ends of a light string of
length 2a. The whole system is
kept on a frictionless horizontal
surface with the string held tight
so that each mass is at a distance
'a' from the centre P (as shown in
the figure).
m m
a a
P
F
Now , the mid-point of the string is pulled vertically upwards
with a small but constant force F. As a result, the particles move
towards each other on the surface. The magnitude of
acceleration, when the separation between them becomes 2x, is
( a)
22 2
Fa
m
ax -
(b)
22 2
Fx
m
ax -
(c)
2
Fx
ma
(d)
22
2
Fax
mx
-
A
B
30º
19. Two blocks are connected over a
massless pulley as shown in fig.
The mass of block A is 10 kg and
the coefficient of kinetic friction is
0.2. Block A slides down the incline
at constant speed. The mass of
block B in kg is
(a) 3.5 (b) 3.3 (c) 3.0 (d) 2.5
20. A light spring balance hangs from the hook of the other
light spring balance and a block of mass M kg hangs from
the former one. Then the true statement about the scale
reading is
(a) both the scales read M kg each
(b) the scale of the lower one reads M kg and of the upper
one zero
(c) the reading of the two scales can be anything but the
sum of the reading will be M kg
(d) both the scales read M/2 kg each
21. Tension in the cable supporting an elevator, is equal to the
weight of the elevator. From this, we can conclude that the
elevator is going up or down with a
(a) uniform velocity (b) uniform acceleration
(c) variable acceleration (d) either (b) or (c)
22. A particle tied to a string describes a vertical circular motion
of radius r continually. If it has a velocity 3gr at the
highest point, then the ratio of the respective tensions in
the string holding it at the highest and lowest points is
(a) 4 : 3 (b) 5 : 4 (c) 1 : 4 (d) 3 : 2
23. A block of mass m is connected to another block of mass M
by  a spring (massless) of spring constant k. The block are
kept on a smooth horizontal plane. Initially the blocks are at
rest and the spring is unstretched. Then a constant force F
starts acting on the block of mass M to pull it. Find the force
of the block of mass m.
( a)
() +
MF
mM
(b)
mF
M
(c)
() +MmF
m
(d)
() +
mF
mM
   
24. A block of mass m is placed on a surface with a vertical
cross section given by 
3
x
y.
6
= If the coefficient of friction
is 0.5, the maximum height above the ground at which the
block can be placed without slipping is:
( a)
1
m
6
(b)
2
m
3
(c)
1
m
3
(d)
1
m
2
25. A ball of mass 10 g moving perpendicular to the plane of the
wall strikes it and rebounds in the same line with the same
velocity. If the impulse experienced by the wall is 0.54 Ns,
the velocity of the ball is
(a) 27 ms
–1
(b) 3.7 ms
–1
(c) 54 ms
–1
(d) 37 ms
–1
26. A block is kept on a inclined plane of inclination q of length l.
The velocity of particle at the bottom of inclined is (the
coefficient of friction is m)
( a)
2 / 1
)] sin cos ( g 2 [ q - q m l (b) ) cos (sin g 2 q m - q l
(c) ) cos (sin g 2 q m + q l (d) ) sin (cos g 2 q m + q l
27. Three forces start acting simultaneously
on a particle moving with velocity, v
r
.
These forces are represented in magnitude
and direction by  the three sides of a
triangle  ABC. The particle will now move
with velocity A
B
C
(a) less than v
r
(b) greater than v
r
(c) |v| in the direction of the largest force BC
(d)
v
r
, remaining unchanged
28. A bullet is fired from a gun. The force on the bullet is given by
F = 600 – 2 × 10
5
 t where, F is in newton and t in second. The
force on the bullet becomes zero as soon as it leaves the
barrel. What is the average impulse imparted to the bullet?
(a) 1.8 N-s (b) zero (c) 9 N-s (d) 0.9 N-s
29. A block of 7 kg is placed on a rough horizontal surface and
is pulled through a variable force F (in N) = 5t, where t is time
in second, at an angle of 37° with the horizontal as shown in
figure. The coefficient of static friction of the block with the
surface is one. If the force starts acting at  t = 0s, the time at
which the block s tarts to s lide is t
0
 sec. Find the value of
t
0
/2 in sec. (g = 10 m/s
2 
and cos 37° = 
4
5
)
/////////////////////////////////////////////////////////
3 7 °
7 kg
F = 5t
(a) 3 (b) 4 (c) 5 (d) 6
30. A stationary body of mass 3 kg explodes into three equal
pieces. Two of the pieces fly off in two mutually
perpendicular directions, one with a velocity of 
1
ˆ
3i ms
-
and the other with a velocity of 
1
ˆ
4jms.
-
 If the explosion
occurs in 10
–4
 s, the average force acting on the third piece
in newton is
( a)
4
ˆˆ
(3i 4j) 10
-
+´ (b)
4
ˆˆ
(3i 4j) 10
-
-´
(c)
4
ˆˆ
(3i 4j) 10-´ (d)
4
ˆˆ
(3i 4j) 10-+´
Page 5


1 . A player stops a football weighing 0.5 kg which comes flying
towards him with a velocity of 10m/s. If the impact lasts for
1/50th sec. and the ball bounces back with a velocity of 15
m/s, then the average force involved is
(a) 250 N (b) 1250 N
(c) 500 N (d) 625 N
2 . A 5000 kg rocket is set for vertical firing. The exhaust speed
is 800 m/s. To give an initial upward acceleration of 20 m/s
2
,
the amount of gas ejected per second to supply the needed
thrust will be (Take g = 10 m/s
2
)
(a) 127.5 kg/s (b) 137.5 kg/s
(c) 155.5 kg/s (d) 187.5 kg/s
3 . A mass ‘m’ is supported by a massless string wound around
a uniform hollow cylinder of mass m and radius R. If the
string does not slip on the cylinder, with what acceleration
will the mass release?
( a)
2g
3
(b)
g
2
m
R
m
(c)
5g
6
(d) g
s w a L 	 f o 	 n o i t o M
J E E 	 n i a M 	 s l a c i r e m u N
4 . A 40 kg slab rests on a frictionless floor as shown in
the figure. A 10 kg block rests on the top of the slab. The
static coefficient of friction between the block and slab
is 0.60 while the coefficient of kinetic friction is 0.40. The
10 kg block is acted upon by a horizontal force of 100 N. If
g = 9.8 m/s
2
, the resultaing acceleration of the slab will be
40 kg
10 kg
B
A
100 N
(a) 0.98 m/s
2
(b) 1.47 m/s
2
(c) 1.52 m/s
2
(d) 6.1 m/s
2
5 . The pulleys and strings shown in the figure are smooth and
of negligible mass. For the system to remain in equilibrium,
the angle q should be
 
q 
m m 
Ö 2 m  
(a)0
o
(b) 30
o
(c) 45
o
(d) 60
o
6 . A satellite in a force free space sweeps stationary
interplanetary dust at a rate (dM/dt) = av. The acceleration
of satellite is
( a)
2
2v
M
-a
(b)
2
v
M
-a
(c)
2
v
2M
-a
(d) – av
2
7 . A monkey is decending from the branch of a tree with
constant acceleration. If the breaking strength is 75% of the
weight of the monkey , the minimum acceleration with which
monkey can slide down without breaking the branch is
(a) g (b)
4
g 3
(c)
4
g
(d)
2
g
mg
q
8 . A plank with a box on it at one end
is gradually raised about the other
end. As the angle of inclination with
the horizontal reaches 30º the box
starts to slip and slides 4.0 m down
the plank in 4.0s. The coefficients of static and kinetic friction
between the box and the plank will be, respectively :
(a) 0.6 and 0.5 (b) 0.5 and 0.6
(c) 0.4 and 0.3 (d) 0.6 and 0.6
9 . A car having a mass of 1000 kg is moving at a speed of 30
metres/sec. Brakes are applied to bring the car to rest. If the
frictional force between the tyres and the road surface is
5000 newtons, the car will come to rest in
(a) 5 seconds (b) 10 seconds
(c) 12 seconds (d) 6 seconds
45° 45°
m 2m
A B
10. Block A of mass m and block B of
mass 2m are placed on a fixed
triangular wedge by means of a
massless, inextensible string and a
frictionless pulley as shown in figure.
The wedge is inclined at 45° to the horizontal on both the
sides. If the coefficient of friction between the block A and
the wedge is 2/3 and that between the block B and the wedge
is 1/3 and both the blocks A and B are released from rest, the
acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
11. The rate of mass of the gas emitted from rear of a rocket is
initially 0.1 kg/sec. If the speed of the gas relative to the
rocket is 50 m/sec and mass of the rocket is 2 kg, then the
acceleration of the rocket in m/sec
2 
is
(a) 5 (b) 5.2 (c) 2.5 (d) 25
12. A block of mass m is resting on a smooth horizontal surface.
One end of a uniform rope of mass (m/3) is fixed to the block,
which is pulled in the horizontal direction by applying a
force F at the other end. The tension in the middle of the
rope is
( a)
8
F
7
(b)
1
F
7
(c)
1
F
8
(d)
7
F
8
13. A body of mass M is kept on a rough horizontal surface
(friction coefficient µ). A person is trying to pull the body
by applying a horizontal force but the body is not moving.
The force by the surface on the body is F, then
(a) F = Mg
(b) F = mMg
(c)
2
Mg F Mg 1 µ££+
(d)
2
Mg F Mg 1 µ³³+
14. Which one of the following motions on a smooth plane
surface does not involve force?
(a) Accelerated motion in a straight line
(b) Retarded motion in a straight line
(c) Motion with constant momentum along a straight line
(d) Motion along a straight line with varying velocity
15. A block A of mass m
1
 rests on a horizontal table. A light
string connected to it passes over a frictionless pulley at
the edge of table and from its other end another block B of
mass m
2
 is suspended. The coefficient of kinetic friction
between the block and the table is µ
k
. When the block A is
sliding on the table, the tension in the string is
( a)
2k1
12
(m – m)g
(mm)
m
+
(b)
12k
12
mm(1 )g
(mm)
+m
+
(c)
12k
12
mm(1– )g
(mm)
m
+
(d)
2k1
12
(m m)g
(mm)
+m
+
16. The upper half of an inclined plane with inclination f is perfectly
smooth while the lower half is rough. A body starting from rest
at the top will again come to rest at the bottom if the coefficient
of friction for the lower half is given by
(a) 2 cos f (b) 2 sin f (c) tan f (d) 2 tan f
17. A particle describes a horizontal circle in a conical funnel
whose inner surface is smooth with speed of 0.5 m/s. What
is the height of the plane of circle from vertex of the funnel?
(a) 0.25 cm (b) 2 cm (c) 4 cm (d) 2.5 cm
18. Two particles of mass m each are
tied at the ends of a light string of
length 2a. The whole system is
kept on a frictionless horizontal
surface with the string held tight
so that each mass is at a distance
'a' from the centre P (as shown in
the figure).
m m
a a
P
F
Now , the mid-point of the string is pulled vertically upwards
with a small but constant force F. As a result, the particles move
towards each other on the surface. The magnitude of
acceleration, when the separation between them becomes 2x, is
( a)
22 2
Fa
m
ax -
(b)
22 2
Fx
m
ax -
(c)
2
Fx
ma
(d)
22
2
Fax
mx
-
A
B
30º
19. Two blocks are connected over a
massless pulley as shown in fig.
The mass of block A is 10 kg and
the coefficient of kinetic friction is
0.2. Block A slides down the incline
at constant speed. The mass of
block B in kg is
(a) 3.5 (b) 3.3 (c) 3.0 (d) 2.5
20. A light spring balance hangs from the hook of the other
light spring balance and a block of mass M kg hangs from
the former one. Then the true statement about the scale
reading is
(a) both the scales read M kg each
(b) the scale of the lower one reads M kg and of the upper
one zero
(c) the reading of the two scales can be anything but the
sum of the reading will be M kg
(d) both the scales read M/2 kg each
21. Tension in the cable supporting an elevator, is equal to the
weight of the elevator. From this, we can conclude that the
elevator is going up or down with a
(a) uniform velocity (b) uniform acceleration
(c) variable acceleration (d) either (b) or (c)
22. A particle tied to a string describes a vertical circular motion
of radius r continually. If it has a velocity 3gr at the
highest point, then the ratio of the respective tensions in
the string holding it at the highest and lowest points is
(a) 4 : 3 (b) 5 : 4 (c) 1 : 4 (d) 3 : 2
23. A block of mass m is connected to another block of mass M
by  a spring (massless) of spring constant k. The block are
kept on a smooth horizontal plane. Initially the blocks are at
rest and the spring is unstretched. Then a constant force F
starts acting on the block of mass M to pull it. Find the force
of the block of mass m.
( a)
() +
MF
mM
(b)
mF
M
(c)
() +MmF
m
(d)
() +
mF
mM
   
24. A block of mass m is placed on a surface with a vertical
cross section given by 
3
x
y.
6
= If the coefficient of friction
is 0.5, the maximum height above the ground at which the
block can be placed without slipping is:
( a)
1
m
6
(b)
2
m
3
(c)
1
m
3
(d)
1
m
2
25. A ball of mass 10 g moving perpendicular to the plane of the
wall strikes it and rebounds in the same line with the same
velocity. If the impulse experienced by the wall is 0.54 Ns,
the velocity of the ball is
(a) 27 ms
–1
(b) 3.7 ms
–1
(c) 54 ms
–1
(d) 37 ms
–1
26. A block is kept on a inclined plane of inclination q of length l.
The velocity of particle at the bottom of inclined is (the
coefficient of friction is m)
( a)
2 / 1
)] sin cos ( g 2 [ q - q m l (b) ) cos (sin g 2 q m - q l
(c) ) cos (sin g 2 q m + q l (d) ) sin (cos g 2 q m + q l
27. Three forces start acting simultaneously
on a particle moving with velocity, v
r
.
These forces are represented in magnitude
and direction by  the three sides of a
triangle  ABC. The particle will now move
with velocity A
B
C
(a) less than v
r
(b) greater than v
r
(c) |v| in the direction of the largest force BC
(d)
v
r
, remaining unchanged
28. A bullet is fired from a gun. The force on the bullet is given by
F = 600 – 2 × 10
5
 t where, F is in newton and t in second. The
force on the bullet becomes zero as soon as it leaves the
barrel. What is the average impulse imparted to the bullet?
(a) 1.8 N-s (b) zero (c) 9 N-s (d) 0.9 N-s
29. A block of 7 kg is placed on a rough horizontal surface and
is pulled through a variable force F (in N) = 5t, where t is time
in second, at an angle of 37° with the horizontal as shown in
figure. The coefficient of static friction of the block with the
surface is one. If the force starts acting at  t = 0s, the time at
which the block s tarts to s lide is t
0
 sec. Find the value of
t
0
/2 in sec. (g = 10 m/s
2 
and cos 37° = 
4
5
)
/////////////////////////////////////////////////////////
3 7 °
7 kg
F = 5t
(a) 3 (b) 4 (c) 5 (d) 6
30. A stationary body of mass 3 kg explodes into three equal
pieces. Two of the pieces fly off in two mutually
perpendicular directions, one with a velocity of 
1
ˆ
3i ms
-
and the other with a velocity of 
1
ˆ
4jms.
-
 If the explosion
occurs in 10
–4
 s, the average force acting on the third piece
in newton is
( a)
4
ˆˆ
(3i 4j) 10
-
+´ (b)
4
ˆˆ
(3i 4j) 10
-
-´
(c)
4
ˆˆ
(3i 4j) 10-´ (d)
4
ˆˆ
(3i 4j) 10-+´
1. (d) Here m = 0.5 kg ; u = – 10 m/s;
t = 1/50 s ; v = + 15 ms
–1
Force = m (v– u)/t = 0.5 (10 + 15) × 50 = 625 N
2. (d) Mass of rocket (m) = 5000 Kg
Exhaust speed (v) = 800 m/s
Acceleration of rocket (a) = 20 m/s
2
Gravitational acceleration (g) = 10 m/s
2
We know that upward force
F = m (g + a) = 5000 (10 +20)
  = 5000 × 30 = 150000 N.
We also know that amount of gas ejected
s / kg 5 . 187
800
150000
v
F
dt
dm
= = = ÷
ø
ö
ç
è
æ
3. (b) From figure,
Acceleration a = Ra …( i)
and mg – T = ma …( ii)
From equation (i) and (ii)
T × R = mR
2
a = mR
2
æö
ç÷
èø
a
R
        
R
m a
a
mg
T
T
or T = ma
Þ mg – ma  = ma
Þ
2
=
g
a
4 . ( a ) Limiting friction between block and slab
= µ
s
m
A
g = 0.6 ×10 × 9.8 = 58.8 N
But applied force on block A is 100 N. So the block will
slip over a slab.
Now kinetic friction works between block and slab
F
k
 = µ
k
m
A
g = 0.4 × 10× 9.8 = 39.2 N
This kinetic friction helps  to move the slab
\ Accleration of slab 
2
B
39.2 39.2
0.98 m/s
m 40
===
5. (c) The tension in both strings will be same due to symmetry .
q q
Tcosq
T
A
mg mg
T
C
T T
Tsinq B
mg Ö2
T c o sq
Tsinq
For equilibrium in vertical direction for body B we have
2 2 cos=qmgT
\
2 2( )cos=q mg mg
      [QT = mg, (at equilibrium]
\
1
cos
2
q= Þ
45q=°
6. (b) Thrust on the satellite,
vdM
Fv(
dt
-
= =- a
Acceleration 
2
Fv
MM
-a
==
7. (c) Let T be the tension in the branch of a tree when
monkey is descending with acceleration a. Then mg –
T = ma; and T = 75% of weight of monkey
m g
4
1
m g
100
75
÷
ø
ö
ç
è
æ
= ÷
ø
ö
ç
è
æ
=
 or 
4
g
a = .
8. (a) Coefficient of static friction,
m
s
 = tan 30° = 
1
3
 = 0.577 @ 0.6
S = ut + 
2
1
at
2
4 = 
1
2
a(4)
2
 Þ a = 
1
2
 = 0.5
[Q s = 4m and t = 4s given]
a = gsinq – m
k
(g) cosq
Þ m
k 
= 
0.9
3
 = 0.5
9. (d)
u
vuatt
a
=-Þ= [ As v = 0]
u m 30 1000
t 6 sec
F 5000
´´
===
10. (d) AW BW
21
;.
33
m=m=
mg
2
mg
2
2mg
2
2mg
2
A
B N
B
T T
mg 2mg
4 5 ° 45°
2 m
m
Diagram shows the various forces acting on the masses
and their resolution in the direction of motion. Let us
consider the two masses to be a system. The forces
trying to move the system such that A moves upwards
and B moves downwards
2mg mg mg
222
=-=
The forces trying to stop this motion (i.e., maximum
frictional force)
= f
A
 + f
B
 
AABB
NN =m +m
2 mg 1 2mg 4 mg
333222
=´+´=
Since the stopping force is more therefore the mass
HINTS & SOLUTIONS