[SECTION-I]
Direction:This section contains multiple choice questions. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE choice is correct.
1. Figure shows a system of three masses being pulled with a force F. The masses are connected to each other by massless strings. The horizontal surface is frictionless. The tension T1 in the first string is 16 N. The acceleration of the system is
F m T1 3m T2 5m (a) m 1 (b) m 2 (c) m 3 (d) m 4
2. Two small balls of same size and masses m1and m2(m1> m2) are tied by a thin weightless thread and dropped from a balloon. The tension T of the thread during the flight after the motion of the balls has become steady will be
(a)
m1m2
g (b)
m m
g 2 2 1 (c)
m m
g 2 1 (d)
g m m 2 2 13. A body whose mass is 13 kg appears 12 kg when weighted by mean of a spring balance is in a moving lift. The value of acceleration with magnitude and direction is
(a)
12g upwards (b) 13g upwards (c) 12g downwards (d) 13g downwards 4. Two small blocks of masses m1and m2connected by a light
inextensible string passing over a smooth pulley are in equilibrium on a fixed smooth wedge. The ratio of the
masses m1and m2is m1 m2 =600 =300 (a) 3 1 (b) 2 1 (c) 3 1 (d) 2 1
5. A parachutist of weight w strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude 3g. Force exerted on him by ground during landing is
(a) 4 w (b) 3 w (c) 2 w (d) w
6. The velocity time graph of a lift moving downwards is a straight line inclined to the time axis
at 450. There is small block of mass m kg in the lift. Then the effective weight of block is (in Newton) (take g = 10 ms–2)
(a) m (b) 9 m (c) 10 m (d) none of these
7. A body climbs up with a speed v on a smooth inclined plane having inclination 300 and stops at a distance of 17.3m. Now if the angle of inclination be 600, then the distance it will go along the inclined plane with the same speed is
8. In the figure shown system is released from rest at time
t= 0, 2 sec after the start, 4 kg block is stopped and is held
stationary. The height to which block 2 kg rises from its position at t = 2s before coming to rest momentarily is (a) gm 9 (b) m g 9 2 (c) mg 3 (d) m g 3 2 2kg 4kg
9. A trolley is being pulled up an incline plane by a man sitting on it (as shown in figure). He applies a force of 250 N. If the combined mass of the man and trolley is 100 kg, the acceleration of the trolley will be [sin 15° = 0.26]
(a) 2.4 m/s2 (b) 9.4 m/s2 (c) 6.9 m/s2 (d) 4.9 m/s2
15° 250 N
10. In the given figure, all strings and pulleys are ideal and acceleration of m1 is
3
g m/s2 upward. Then find the ratio of
m1/m2. (a) 3 1 (b) 1 (c) 2 1 (d) 4 1 m2 m1
11. Consider the situation shown in the figure. The acceleration of mass m is
(a) g/3 up the plane (b) g/3 down the plane (c) g/2 up the plane (d) g/2 down the plane
300
2m
m
12. In the figure a block of mass M is at rest on the floor. The acceleration with which should a boy of mass m climb along the rope of negligible mass, so as to just lift the block from the floor is
(a) equal to g m M 1 (b) greater than g m M 1 (c) equal to g m M (d) greater than g m M B M a m
13. A block of mass m is placed on a smooth inclined plane of inclination with the horizontal. The force exerted by the plane on the block has a magnitude
14. A block of wood is kept on the floor of a stationary elevator. The elevator begins to descend with an acceleration of 12 ms–2. If g = 10 ms–2, then the displacement of the block during the first 0.2 second after the start is
(a) 0.02 m (b) 0.1 m (c) 0.2 m (d) 0.4 m
15. A balloon contains 10 g of air. The air begins to escape from a small hole in the balloon at the steady rate of 4 cms–1and it completely shrinks in 2 seconds. Then the average force on the balloon?
(a) 20 dyne (b) 15 dyne (c) 10 dyne (d) 5 dyne 16. In the Atwood machine (data as in figure) P is a
massless pulley, and springs S1 and S2 are also massless. If the blocks are set free to move, the readings in S1and S2respectively be
(a) kg 3 2 kg; 3 1 (b) kg 3 4 kg; 3 4 (c) kg 3 4 kg; 3 2 (d) kg 3 2 kg; 3 2 1kg 2kg S2 S1 P
17. Two masses m and M are connected by a light string passing over a smooth pulley. When the system set free m moves up by 1.4 m in 2 s. The ratio M/m is
(a) 17/3 (b) 15/13 (c) 9/7 (d) 7/9
18. In the system, the m1 = 300 gm, m2 = 500 gm and
F = 1.7N. If the mass and friction of pulley are
negligible, then the acceleration of m2is (a) 9.8 m/s2 (b) 1 m/s2 (c) 1.7 m/s2 (d) 0.88 m/s2
m2
m1 F
19. As shown in the figure, two blocks of masses 3 kg and 6 kg are connected by a string of mass 1 kg and placed on a frictionless surface. The system is pulled from the side of block 3 kg with a constant force 20 N. Tension in the string at points A, B and C is
20N 3kg 1kg 6kg
A B C
(a) 16 N, 14 N, 12 N (b) 14 N, zero, 12 N (c) 14 N, 12 N, 10 N (d) 14 N, 13 N, 12 N
20. The potential energy of a conservative system is given by U = ay2– by, where y represents the position of the particle and a as well as b are constants. The force acting on the system will be
(a) b2ay (b) 2ay b (c) by (d) ay
21. In the given arrangement, n number of equal masses are connected by strings of negligible masses. The tension in the string connected to nth mass is (friction is absent every where)
m m m m m M n 4 3 2 1 (a) M nm mMg (b) nmM mMg (c) mg (d) mng
22. The 50 kg homogeneous smooth sphere rests on the 300incline A and bears against the smooth vertical wall
B. The contact force at B is (g = 10 m/s2)
(a) 250 N (b) zero (c)
N
3
500
(d) 500 N B A 30023. In the given massless and frictionless pulley system, (a) tension in both the strings is zero
(b) pulleys B and C rotate counter clockwise and the pulley A clockwise
(c) acceleration of A and B are same and is equal to 2g (d) all of the above
C m1 m2
B A
24. Two bodies A and B of masses m1and m2 respectively are connected by a massless spring of force constant k. A constant force F starts acting on the body A at t = 0. Then
A B
m2 m1
k
(a) at every instant, the acceleration of centre of mass is
2 1 m
m F
(b) at t = 0, acceleration of B is zero but that of A is maximum (c) the acceleration of A decreases continuously
(d) all of the above
25. A solid sphere of mass 2 kg is resting inside a cube in the vertical plane as shown in the figure. The cube is moving with a velocityv
5tiˆ2t ˆj
m/s. Here t is the time in second. All surfaces are smooth. The sphere is at rest with respect to the cube. What is the total forceexerted by the sphere on the cube? (take g = 10 m/s2) x
y
O
A B
D C
26. The variation of momentum with time of one of the body in a two body collision is shown in the figure. The instantaneous force is maximum corresponding to point
(a) P (b) Q (c) R (d) S P Q R S P t 27. Figure shows the displacement of a particle going along
the X-axis as a function of time. The force acting on the particle is zero in the region.
(a) AB (b) BC (c) CD (d) DE x t A B C D E
28. Which of the following graph depicts spring constant k versus length l of the spring correctly? (a) k I (b) k I (c) k I (d) k I
29. A car A is at a distance 10 m from the car B towards north direction. Car A moves towards east with 40 m/s. Car B moves towards north with 30 m/s. The minimum distance between A and B will be
(a) 10m (b) 8 m (c) 6 m (d) 30 m
30. The velocity-displacement graph (v-x graph) of the motion of particle is shown in the figure. The acceleration-displacement graph (a-x graph) of the motion of the particle is
v x v0 x0 a x (a) a x (b) a x (c) a x (d)
31. A ship moves along the equator to the east with a velocity of 30 km/hour. The south eastern wind blows at an angle of 600to the equator with a velocity of 15 km/hr. The wind velocity relative to the ship (take cos 600= 0.500 and sin 600= 0.866) is
(a) 35 km /hr nearly (b) 60 km /hr nearly (c) 26 km /hr nearly (d) 50 km /hr nearly
32. Acceleration of a body moving along a straight line varies with time as shown in the figure. If velocity at
t= 7.5 sec is 25 m/sec, velocity at t = 15 sec will be
(a) 50 m/s (b) zero (c) 35 m/s (d) 44 m/s t(s) a (m /s 2 ) 5 7.510 15
33. The 5 kg cart at rest at t = 0 is acted on by a horizontal force which varies with time as shown. Neglect friction. The velocity of the cart at t = 1 second is
(a) 1 m/s (b) 0.5 m/s (c) 3 1 m/s (d) 6 1 m/s 20 Parabolic Force F(N) Time t(s) 2
34. A rod length l slides down along an inclined plane and the ground as shown in the figure. At any instant the velocity of end B is v, then the velocity of end A at the same instant will be
(a) sin sin v (b) cos cos v (c) vcos
(d) vcos
u A B v35. A particle is projected with a velocity v at an angle to the horizontal. At a certain point of its trajectory, its velocity makes an angle
2
with the horizontal. The radius of curvature of this point is (a) 2 cos 2 g v (b) 2 cos cos 2 2 g v (c) 2 cos cos 2 3 2 g v (d) 2 cos cos 3 2 2 g v
36. A point moves along an arc of a circle of radius R. Its velocity varies as v a s where a is
constant. The angle between the vector of total acceleration and the vector of velocity is given by (a) s R 1 tan (b) s R 2 tan 1 (c) R s 2 tan 1 (d) R s 1 tan
37. A body moves according to the equation
2 1
t
S . Which one of the following
statements is true
(a) acceleration is positive and proportional to rd
3 5 power of velocity
(b) acceleration is positive and proportional to 5 3 th power of velocity (c) velocity is proportional to 3 1 rd power of distance (d) velocity and acceleration have the same sign
38. A particle moves along a circular path of radius r with uniform speed v. The angle described by the particle in one second is given by
39. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is
(a) 1 (b) 3 (c) 4 (d) 41
40. A rod AB is moving in a vertical plane. At a certain instant when the rod is inclined at 60° to the horizontal, the point A is moving horizontally at 3 m/s, while B is moving in the vertical direction. The velocity of B is
A vA B vB 60° (a) 3 1 m/s (b) 2 3m/s (c) 3 m/s (d) 2 3 m/s
41. A particle is projected vertically upwards from a point A on the ground. It takes t1seconds to reach a point B at a height h from A bit still continues to move up. If it takes further t2 seconds from B to ground again, then h is equal to
(a) 2 2 1 2 1 t gt (b)
2 2 1 2 1 t t g (c) 1 2 2 1 t gt (d) 12 2 2 1 t gt42. An object is projected up the incline with speed 30 m/s at an angel 300 as shown in the figure. The distance s up the incline at which the object lands is (g = 10 m/s2) (a) 6.0 m (b) 60 m (c) 120 m (d) 600 m 30 300 0 B s 30 m/s
43. A car is moving towards east with a speed of 25 km/hr. To the driver of the car, a bus appears to move towards north with a speed of
25
3
km/hr. The actual velocity of the bus is(a) 50 km/hr, 300east of north (b) 50
3
km/hr, 300east of north(c) 50 km/hr, 300west of north (d) 50
3
km/hr, 300west of north44. Second’s hand of a clock is 6 cm long. As shown in the figure, A is a point on the second hand at a distance 3 cm from centre. The change in velocity of
Ain 15 s will be 3cm A O (a) 10 2 cm/s (b) 10 2 cm/s (c) 30 2 cm/s (d) zero
45. A body is moving along a straight line. Its speed varies with time as shown in the figure. Average speed of the body for its motion from t = 0 to t = t1is (a) 10 m/s (b) 5 m/s (c) 2.5 m/s (d) 7.5 m/s 10 5 3 sin1 2 1 sin1 t(s) V (m /s ) t1
46. A particle moves along a straight line and at a distance x from a fixed point O on the line, its velocity is
xx then its acceleration is
(a) directed towards O and proportional to
x
1
(b) directed towards O and is proportional to 12
x
(c) directed away from O and is proportional to x (d) directed away from O and is proportional to x2
47. A ball is thrown upward at an angel 300 to the horizontal and lands on the top edge of a tower that is 20 m away and 5m high. The thrown velocity is (a) 10 m/s (b) 20 m/s (c) 40 m/s (d) 80 m/s 300 v0 O 5m 20m
48. Displacement-time graph of a body confined to move along a straight line is as shown in the figure. Which of the following graph represents the correct velocity-time variation. s t t1 t2 t3 t4 t5 v t t1 t2 t3 t4 t5 (a) v t t1 t2 t3 t4 t5 (b) v t t1 t2 t3 t4 t5 (c) v t t1 t2 t3 t4 t5 (d)
49. A body starts from rest at t = 0 and moves along a straight line. Its acceleration is given as
t
a . The body travels a distance of 30m from t = 1 s to t = 2 s. Distance travelled during
the fourth second is (approx.)
(a) 159 m (b) 250 m (c) 350 m (d) 210 m
50. Two particle are projected horizontally in opposite directions from the same height at t = 0 with velocities 12 m/s and 3m/s. Relative speed of the two when there velocities become mutually perpendicular is (g = 10 m/s2)
(a) 15 m/s (b) 12 m/s (c) 10 m/s (d) 9 m/s
51. A lift is going up. The variation in the speed of the lift is as given in the graph. What is the height to which the lift takes the passengers
(a) 3.6 m (b) 28.8 m (c) 36.0 m
(d) Cannot be calculated from the above graph
0 2 Time (sec) 10 12 3.6 V el oc ity ( m /s ec )
52. Cars X and Y start their journey from the same place with X leaving 3 minutes earlier than
Y. The cars move in the same direction with equal accelerations. Time taken after the
departure of X so that the distance travelled by
16 1
Y the distance travelled by X, is
(a) 240 sec (b) 180 sec (c) 100 sec (d) 120 sec
53. Velocity-time (v-t) graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration and retardation is (a) 60 m (b) 50 m (c) 30 m (d) 40 m t (sec) V (m /s ) 10 20 40 50 0 1 2 3 4 30 60
54. Mass of a spherical object (10±1)g. Its radius is 3 1 3
cm with a percentage error of 2%. Density of the object can be expressed as
(a) (2.5 ± 0.6)g/cm3 (b) (2.5 ± 0.8)g/cm3 (c) (2.5 ± 0.4)g/cm3 (d) (2.5 ± 0.3)g/cm3 55. In the following graph, distance travelled by the body
in metres is (a) 200 (b) 250 (c) 300 (d) 400 Time (s) v (m /s ) 10 30 0 5 10 20 40 Y 15 X
56. An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement (s) – velocity (v) graph of this object is
(a) s v (b) s v (c) s v (d) s v
57. The graph of displacement vs time is s
t
(a) v t (b) v t (c) v t
(d) v t 58. A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its height if the air resistance is ignored
(a) S pe ed Time (b) Spe ed Time (c) Spe ed Time (d) Spe ed Time
59. Which graph represents the uniform acceleration?
(a) s t (b) s t (c) s t (d) s t
60. Which of the following velocity-time graphs shows a realistic situation for a body in motion?
(a) v t (b) v t (c) v t (d) v t 61. Acceleration-time graph of a body is shown. The
corresponding velocity-time graph of the same body is a t (a) v t (b) v t (c) v t (d) v t
62. An object starts from rest at t = 0 and moves along a straight line. From t = 0 to t = 3 sec, it moves with an acceleration a1 and travels a distance 10m; from t = 3 sec to t = 6 sec, it moves with an acceleration a2and travels 25m; from t = 6 sec to t = 9 sec; it covers 52 m with acceleration a3. Which of the following is correct.
(a) a1 a2 a3 (b) a1 a2 a3 (c) a3 a2 a3 (d) a2 a1a3
63. The acceleration-time graph of a body is shown below. The most probable velocity-time graph of the body is a t (a) v t (b) v t (c) v t (d) v t
64. A shell is fired from a gun with an initial velocity v at an angle with horizontal. At the highest point of trajectory, the shell explodes into two fragments X and Y of equal masses.
Given that the speed of fragment X, immediately after the explosion, is zero, the distance from the gun does the fragment Y strike the ground is
(a) g v2sin2 (b) g v sin2 2 3 2 (c) g v sin2 2 5 2 (d) g v sin2 2 2
65. A boy whirls a stone in a horizontal circle 2 m above the ground by means of a string 1 m long. The string breaks and the stone flies off horizontally striking the ground 10 m away. The acceleration (in m/s2) during the circular motion is (g = 10 m/s2)
(a) 250 (b) 200 (c) 150 (d) 100
66. A motor car has its centre of gravity 1 m above the ground and its wheels are 1.5 m apart. The safe speed at which it negotiates at a level curve of radius 40 m is
(a) 9.8 m/s (b) 98 m/s3 (c) 1.5 m/s (d) 98 m/s
67. Three blocks of same mass are connected through string as shown in the figure. The values of f1, f2 are (take g = 10 m/s2 and all strings and pulleys are ideal) (a) 24 N, 28 N (b) 20 N, 28 N (c) 24 N, 20 N (d) 20 N, 20 N 4kg = 0.7 4 kg 4kg f1 f2 = 0.6
68. A particle is moving in a circle of radius R in such a way that at any instant, the normal and tangential components of its acceleration are equal. If its speed at t = 0 is v0, the time taken to complete the first revolution is
(a) 0 v R (b)
2
0 1 e v R (c) 2 0 e v R (d) 0 2 v R 69. A train is moving with a speed v on a curved railway track of radius r. A spring balance loaded with a block of mass m is suspended from the roof of the train. The reading of the spring balance is (a) m (b) rg mv2 (c) rg mv m 2 (d)
2 2 2 rg mv m70. A block of mass 4 kg is kept on a rough horizontal surface with coefficient of friction = 0.4 and a time varying horizontal force F = 4 t applied on it, then the acceleration time graph of the particle is (g = 10 m/s2) 4kg F = 4t a t 4s (a) a t 4s (b) 1m/s2 a t 4s (c) a t 4s (d) 1m/s2
71. A block of mass 2 kg start moving with speed 10 m/s at
t = 0 on a rough horizontal surface with coefficient of
friction 0.2 and a constant force 2 N is also applied opposite to motion of particle at t = 0. Find speed of the particle after 4s. (g = 10 m/s2)
(a) 2 m/s (b) zero
2kg =0.2
72. In the arrangement shown in the figure, there is a friction force between the blocks of masses m and 2m. Block of mass 2m is kept on a smooth horizontal plane. The mass of the suspended block is m. Block A is stationary with respect to block of mass 2m. The minimum value of coefficient of friction between m and 2m is
(a) 1 /2 (b) 1/ 2 (c) 1 / 4 (d) 1 /3 m 2mm C A B
73. A 5 million kg ship rests on launching way that slope down to the water at an angle of 100. If the coefficient of sliding friction is 0.2, the force which is required to move down the ship into water is (given g = 10 m/s2, sin 100= 0.17, cos 100= 1)
(a) 1.5 106 N (b) 1.3 106N (c) 1.8 106N (d) 1.7 106N 74. A block of mass m is released on a smooth inclined
surface of wedge of mass M. Find the minimum value of coefficient of friction between wedge and horizontal surface to keep wedge stationary.
M m (a)
M m
m 2 2 sin (b) m M m 2 sin (c)
2 cos 2 2 sin m M m (d)
cos 2 2 sin m M m75. Two beads of masses m1 and m2 are connected by a light rigid rod. The system is placed between a rough floor and smooth vertical wall. The coefficient of friction between the rough floor and the bead of mass m2 is . Which of the following is correct?
(a) the minimum value of so that the system does not slip is 45° N1 m1 T T smooth Rough m2 N2 (b) N1 sinT (c) N2 sinT
(d) N2 N1, when the rod is about to slip
76. Two rods are moving perpendicular to each-other along the axis one on the other with velocities v and 2v, as shown in the figure. The unit vector along which the friction force on the rod moving with velocity v by the rod moving with velocity 2v will act is
(a)
iˆ 2jˆ
5 1 (b)
iˆ 2jˆ
5 1 (c)
3iˆ 2jˆ
5 1 (d)
3iˆ 2jˆ
5 1 y v 2v x
iˆ
jˆ77. A block of mass 1 kg is placed on a rough horizontal surface connected by a light string passing over two smooth pulleys as shown. Another block of 1kg is connected to the other end of the string. The acceleration of the system is
(coefficient of friction = 0.2)
1kg
1kg
(a) 0.8 g (b) 0.4 g (c) 0.5 g (d) zero
78. The angle of an inclined plane is and the angle of friction is ( > ). The acceleration of a body down the plane is
(a)
cos sin g (b)
cos sin g(c) gsin (d) g
sin cos
79. Two blocks A and B having equal mass, are placed in contact with each other on a rough plane, inclined at an angle with horizontal as shown in figure. If coefficients of friction for these blocks are 1 and 2 (1> 2) respectively, then for static equilibrium of two blocks
A
B
(a) cannot be greater than tan–1( 2) (b) cannot be less than tan–1(
2)
(c) maximum possible value of is equal to tan–1 2 2 1
(d) maximum possible value of is equal to tan–1 2 1
80. A simple pendulum is suspended from the ceiling of a trolley. As shown, the trolley is moving towards right with a block of mass 2 kg in contact with its vertical side and with such an acceleration that the block is just prevented from falling under gravity. Coefficient of friction between the surfaces of trolley and the block being
2 1
, inclination of the pendulum to the vertical will be
2kg a (a) 2 1 sin 1 (b) 5 2 sin 1 (c) 5 2 cos 1 (d) 2 1 tan 1
81. A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with vertical is (take g = 10 m/s2)
(a) zero (b) 30° (c) 45° (d) 60°
82. A body of mass 10 kg is moving along a circular path of radius 100m. Its speed increases, in a uniform manner, from 17 m/s to 26m/s in a time duration of 3s. Force acting on the body when it is travelling at a speed 20 m/s is
83. A block of mass m, lying on a rough horizontal plane, is acted upon by a horizontal force P and another force Q, inclined at an angle to vertical. The block will remain in equilibrium, if minimum coefficient of friction between it and surface is
Q
P m
(a) (P + Q sin) / (mg + Q cos ) (b) (P cos + Q) / (mg – Q sin ) (c) (P + Q cos) / (mg + Q sin ) (d) (P sin – Q) / (mg – Q cos )
84. A particle of mass m is fixed to one end of a light spring of force constant K and unstretched length l. The system is rotated, about an axis passing through the other end of the spring with an angular velocity , in gravity free space. The increase in length of the spring will be
K m (a) K l m2 (b) 2 2 m K l m (c) 2 2 m K l m (d)
K l m1285. A body is moving down along inclined plane of slope 370. The coefficient of friction between the body and plane varies as = 0.3x, where x is distance travelled down the plane. The body will have maximum speed (
5 3 37
sin 0 and g 10m/s2)
(a) at x = 1.16 m (b) at x = 2 m (c) at x = 1.25 m (d) at x = 2.5 m
86. A right circular cone is fixed with its axis vertical and vertex down. A particle in contact with its smooth inside surface describes circular motion in a horizontal plane at a height of 20 cm above the vertex. Its velocity in m/s is
(a) 1 (b) 1.2
(c) 1.4 (d) 1.6
h=20cm
87. An automobile car rounds a curve of 80 m radius without slipping, if the road is unbanked and the coefficient of friction between the road and tyres is 0.81. The maximum speed is (a) 12.1 m/s (b) 25.2 m/s (c) 50.4 m/s (d) 75.6 m/s
88. A mass m is hung vertically by means of a thread. It is in contact with vertical surface of a pan as shown. The coefficient of friction between mass m and the pan is . The pan is pulled horizontally with acceleration (a = g) on a smooth horizontal surface. Then the tension in the thread is
m
Pan
a=g
89. A block of mass 2 kg is kept on the floor. The coefficient of static friction is 0.4. If a force F of 2.5 N is applied on the block as shown in the figure. The frictional force between the block and the floor will be
F
(a) 2.5 N (b) 5 N (c) 7.84 N (d) 10 N
90. Two blocks A and B of masses m and M are placed in a platform as shown in the Figure. The friction coefficient between A and B is but there is no friction between B and the platform. The whole arrangement is placed inside an elevator which is coming down with an acceleration f (f < g). What maximum horizontal force F can be applied to A without disturbing the equilibrium of the system?
(a) 2mg (b) 2m(g – f ) (c) 2m(g + f ) (d) 2mf M m F A B T f
91. A given object takes n times as much time to slide down a 45° rough incline as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is given by
(a) 1 12 n (b) 1 2 1 n (c) 2 1 1 n (d) 2 1 1 n
92. On a dry road, the maximum permissible speed of a car along a circular path is 10 m/s. If the road becomes wet, the maximum permissible speed along same path becomes
2
5 m/s. If the coefficient of friction of dry road is , then that for the wet road is (a) 2 (b) 3 (c) 3 2 (d) 4 3
93. A block of mass m is placed on a rough horizontal surface. The coefficient of friction between them is . An external horizontal force is applied to the block and its magnitude is gradually increased. The force exerted by the block on the surface is R, then which of the following statement is incorrect.
(a) The magnitude of R will gradually decrease. (b) R mg 2 1.
(c) The angle made by R with the vertical will gradually increase. (d) The angle made by R with the vertical tan–1.
94. In figure two blocks M and m are tied together with an inextensible string. The mass M is placed on a rough horizontal surface with coefficient of friction and the mass m is hanging vertically against a smooth vertical wall.
M
m
Rough ()
(a) the system will accelerate only when m > M (b) when m < M, T = mg
(c) when m > M, Mg < T< mg (d) all of the above are correct
95. A block of mass 10 kg is placed in a box as shown in figure. Box is moving with constant acceleration of 5 m/s2at an angle of 530from x axis (horizontal direction). Force exerted by box on block in y-direction (vertical direction) will be (g = 10 m/s2, tan 530 = 4/3 )
(a) 140 N (b) 40 N (c) 50 N (d) 150 N 10kg 530 x y a
96. A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is . If the mass is pulled by a force P as shown in the figure, the limiting friction between body and surface will be m 30° P (a)mg (b) 2 μ mg P (c) 2 μ mg P (d) 2 3 μ mg P
97. 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 kinetic friction is 0.40. The 10 kg block is acted upon by a horizontal force 100 N. If g 9.8m/s2, the resulting acceleration of the slab will be
40 kg 10 kg
100 N A
B
(a) 0.98 m/s2 (b) 147 m/s2 (c) 1.52 m/s2 (d) 6.1 m/s2
98. A uniform chain of mass M and length L is placed such that a part of its lies horizontally on a table and the other part hangs along the vertical as shown in figure. Coefficient of limiting friction being =0.25, what maximum percent of total length could hang vertically without sliding the remaining part?
(a) 20% (b) 30% (c) 25% (d) 50%
99. A 50 kg sphere is projected vertically upwards with a speed of 200 m/s. It rises upto a height of 1500 m. The energy used up in overcoming friction is (take g = 9.8 m/s2)
(a) 3.65 104J (b) 3.75 106J (c) 4.75 104J (d) 2.65 105J
100. A particle of mass m is released from rest at point A along the inside surface of a smooth hemispherical bowl of radius R. The speed at B which is at a height
3 2R
h from the lowest point is
A B 2R/3 (a) 2gR (b) 3 4gR (c) gR (d) gR 3 2
101. A block of mass m initially at rest dropped from a height h on to a massless spring of force constant
k, the maximum compression in the spring is h/4,
then spring constant k is (a) h mg 40 (b) h mg (c) h mg 2 (d) h mg 20 m h
102. A ladder 3 m long and weighing 200 N has its centre of gravity 120 cm from the bottom. At its top end is a 50 N weight. The work required to raise the ladder from a horizontal position on the ground to a vertical position is
(a) 290 J (b) 390 J (c) 240 J (d) 150 J
103. If a force F varies with displacement x as F = 3x2 + 4. The work done by force if particle moves from x = 2 to x = 4m is
(a) 64 J (b) 128 J (c) 32 J (d) none of these
104. A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The
equation relating and is
r
A
B
(a) 3sin2cos (b) 2sin3cos (c) 3sin2cos (d) 2sin3cos
105. 1 kg block collides with a horizontal weightless spring of force constant 100 N/m, as shown in the figure. The block compresses the spring 0.4 m from the rest position. Assuming that the coefficient of kinetic friction between the block and the horizontal surface is 0.9, the speed of the block at the instant of collision is approximately (g = 10 m/s2)
M v0
(a) 5 m/s (b) 5.6 m/s (c) 1.4 m/s (d) 5.8 m/s
106. A small body slides without friction from the top of a hemisphere of radius R. It leaves the hemisphere when it has descended a vertical distance of
(a) 4 R (b) 3 R (c) 2 R (d) R
107. Two bodies have same kinetic energy. They are stopped by applying same retarding force. The stopping distance is small for
(a) lighter one (b) heavier one (c) same for both (d) cannot be predicated
108. In hydrogen atom the radius of the orbit of electron changes from r1 to r2 and angular frequency changes from 1to 2. The ratio of 1to 2will be
(a) r1/r2 (b) (r1/r2)2 (c) (r2/r1)2 (d) (r2/r1)3 109. Two bodies of masses m and 4 m are attached with
string as shown in the figure. The body of mass m hanging from a string of length l is executing oscillations of angular amplitude 0, while the other body is at rest.
The minimum coefficient of friction between the mass 4 m and the horizontal surface should be
m 4m 0 l (a) 3 cos 2 0 (b) 2 cos 2 2 0 (c) 2 cos 1 0 (d) 4 cos 2 3 0
110. A stone of mass 1 kg tied to a light inextensible string of length 3 10
L m, whirling in a
circular path in a vertical plane. The ratio of maximum tension in the string to the minimum tension in the string is 4. If g is taken to be 10 m/s2, the speed of the stone at the highest point of the circle is
(a) 10 m/s (b) 5 2m/s (c) 10 3 m/s (d) 20 m/s
111. A person of mass 60 kg carries a 15 kg body on the top of building 10 m high in 5 minutes. He puts a power in carrying the body (g = 10m/s2)
(a) 10 W (b) 25 W (c) 30 W (d) 15 W
112. A 50 g bullet moving with a velocity of 10 ms–1gets embedded into a 950 g stationary body. The loss in kinetic energy of the system will be
(a) 100% (b) 95% (c) 50% (d) 5%
113. Potential energy associated with a conservative force is given by U = Ax2 where A is a constant then
(a) force always tends to accelerate the particle towards origin (b) force always tends to accelerate the particle away from origin
(c) force always tends to accelerate the particle towards the origin if A is positive (d) force always tends to accelerate the particle towards the origin if A is negative
114. A small block of mass m lying at rest at point P of a wedge having a smooth semi circular track of radius R. What should be the minimum value of horizontal acceleration a0of wedge so that mass can just reach the point Q?
Q m P a0
(a) g/2 (b) g (c) g (d) not possible
115. A particle hanging by a light string of length l is projected horizontally from its lowest position with a velocity
2 7gl
. The string slackens after swinging through
(a) 300 (b) 450 (c) 1200 (d) 1500
116. A motor pump 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, by what amount the power of motor must be increased?
117. If the centre of gravity of an object which is slightly disturbed and the object returns to its original position when the disturbing force is removed, the object is said to be in
(a) neutral equilibrium (b) stable equilibrium (c) unstable equilibrium (d) none of these
118. A force of 0.5 N is applied on upper block as shown in figure. The work done by lower block on upper block for a displacement 3m of the upper block is (take g = 10 m/s2)
Smooth 2kg
1kg F = 0.5N = 0.1
(a) 1 J (b) –1 J (c) 2 J (d) –2 J
119. An elastic string of unstretched length L and force constant k is stretched by a small x. It is further stretched by another small length y. The work done in the second stretching is (a) 2 2 1 ky (b)
2 2
2 1 y x k (c)
2 2 1 y x k (d) ky
2xy
2 1120. A body of mass m dropped from a height H reaches the ground with a speed of1.2 gH .
Calculate the work done by air friction.
(a) 0.28 mgH (b) 0.72 mgH (c) – 0.28 mgH (d) – 0.72 mgH
121. The potential energy of particle of mass 0.1 kg moving along the x-axis is given by
4
J5
x x
U , where x is in metre. It can be concluded that (a) the particle is acted upon by a constant force
(b) the speed of the particle is maximum at x = 2m (c) the particle cannot execute simple harmonic motion (d) the period of oscillation of the particle is s
20
122. ABCDE is a smooth iron track in the vertical plane. The
sections ABC and CDE are quarter circles. Points B and D are very close to C. M is a small magnet of mass m. The force of attraction between M and the track is F, which is constant and always normal to the track. M starts from rest at A
A E O C B D r M r ' O
(a) If M does not leave the track if F 2mg.
(b) At B, the normal reaction of the track is F mg
(c) At D, the normal reaction of the track is F mg
(d) The normal reaction of the track is equal to F at stone point between A and B.
123. Two small balls of masses m and 2m are suspended by light wires of length l, so that they are in contact as shown in figure. Coefficient of restitution between two balls is 1/2. Minimum horizontal velocity that should be imparted to the ball of mass 2m so that ball of mass m can perform a complete revolution is
(assuming only one collision take place) 2m m
l
124. A body of mass m was slowly pulled by a force which at each point was directed along a tangent to the path. The work done by the applied force
(a) does not depend upon path followed upon path (b) depends upon path
(c) does not depend upon positions of A and B (d) both (a) and (c) are correct
B
A
F
125. Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35 m is equal to (a) 50 J (b) 25 J (c) 300 J (d) 200 J 5 0 15 10 5 10 15 20 25 30 35 40 F or ce ( N ) Displacement (m) 126. A 10 kg mass moves along x-axis. Its acceleration as
a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8 cm?
(a) 8 × 10–2joules (b) 16 × 10–2joules (c) 4 × 10–4joules (d) 1.6 × 10–3joules 5 0 15 10 2 4 6 8 a ( cm /s ec 2 ) 20 x (cm)
127. Two identical cylindrical shape vessels are placed, A at ground and B at height h. Each contains liquid of density and the heights of liquid in A and B are h1 and h2respectively. The area of either base is A. The total potential energy of liquid of system with respect to ground is (a)
2 2
2 2 1 2 2 h h hh g A (b)
2 2 2 1 2 h h h g A (c) hAg
h1hh2
(d) 1 22 2 2 h h h g A 128. 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 0
10
4 8 12 x (m)
F(N)
129. A particle is dropped from a height h. A constant horizontal velocity is given to the particle. Taking g to be constant every where, kinetic energy E of the particle w.r.t. time t is correctly shown in (a) E t (b) E t (c) E t (d) E t 130. The adjoining diagram shows the velocity versus time plot
for a particle. The work done by the force on the particle is positive from (a) A to B (b) B to C (c) C to D (d) D to E A v t D E B C
131. 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)kxax3. Here k and a are positive constants. For x0, the functional from of the potential energy
) (x U of the particle is (a) U(x) x (b) U(x) x (c) U(x) x (d) U(x) x
132. A force F acting on an object varies with distance x as shown here. The force is in Newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6m is (a) 4.5 J (b) 13.5 J (c) 9.0 J (d) 18.0 J 0 2 1 2 3 4 3 x (m) F(N) 1 5 6 7
133. The potential energy of a system is represented in the first figure. The force acting on the system will be represented by U(x) a x (a) F(x) a x (b) F(x) a x (c) F(x) a x (d) F(x) a x
134. A heavy elastic ball X falls freely from a height h on to a smooth horizontal elastic surface. When X strikes the surface, another ball Y is dropped from the same height, they meet after (a) s g h 2 (b) s g h 2 (c) hs g 2 (d) gs h
135. A 40 kg skater moving at 4 m/s overtakes a 60 kg skater moving at 2 m/s in the same direction and collides with him. Both the skaters move with the same velocity after collision. How much K.E. is lost?
(a) 392 J (b) 48 J (c) 440 J (d) 832 J
136. The kinetic energy of rotation E depends upon the angular momentum J and moment of inertia l . Find the expression for kinetic energy (K is a constant)
(a) 22 I KJ E (b) 2 3 I KJ E (c) E KIJ2 (d) I KJ E 2
137. Two negatively charged particles having charges e1 and e2 and masses m1 and m2 respectively are projected one after another into a region with equal initial velocity. The electric field E is along the y-axis, while the direction of projection makes an angle with the y-axis. If the ranges of the two particles along x-axis are equal then one can conclude that
y
O E
C x
(a) e1e2 and m1m2 (b) e1e2 only (c) m1m2 only (d) e1m1e2m2 138. A mass 2m rests on a horizontal table. It is attached to
a light inextensible string which passes over a smooth pulley and carries a mass m at the other end. If the mass m is raised vertically through a distance h and is then dropped, what is the speed with which the mass 2m begins to rise? 2m m h (a) 5 2gh (b) 3 2gh (c) 3 gh (d) gh 2
139. A body thrown up vertically with velocity u reaches the highest point in t sec. The mean value of the force of air resistance acting on the body during ascent is
(a) mg (b) t mu (c) g t u m (d) t g u m
140. Two blocks of mass 3kg and 6kg are placed on a smooth horizontal surface. They are connected by a light spring of spring constant k = 200 N/m. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. The maximum extension of the spring will be
3kg 6kg
1.0m/s 2.0m/s
(a) 30 cm (b) 25 cm (c) 20 cm (d) 15 cm
141. The momentum of a particle is given by P (4sintiˆ4cost ˆj)kg m/s. Select the correct
alternative
(a) Momentum P of the particle is always parallel to F. (b) Momentum P of the particle is always perpendicular to F. (c) Magnitude of momentum P is variable.
(d) None of the above.
142. A particle moves on a rough horizontal ground with some initial velocity say v0. If (3/4)thof its kinetic energy is lost due to friction in time t0 then coefficient of friction between the particle and the ground is
(a) 0 0 2gt v (b) 0 0 4gt v (c) 0 0 4 3 gt v (d) 0 0 gt v
143. A block moving with velocity u collides with two identical block placed in the track of first block, after
the elastic collision, m
m m
(a) 1st stops, 2nd and 3rd moves with velocity 2 u
(b) 1st and 2nd stops, 3rd moves with velocity u. (c) 1st returned with velocity
2 u
, 2nd moves with velocity 2 u
and 3rd with velocity u. (d) None of these
144. A block of mass m is pushed with a velocity u towards a movable wedge of mass m and height h. All the surfaces are smooth. The minimum value of u for which the block will reach the top of wedge is
(a) 2gh (b) 2gh (c) 1 1 2gh (d) 1 1 2gh m h m u
145. A block A of mass m moving at a speed v collides with another block B of mass 2 m at rest. The block A comes to rest after collision. The coefficient of restitution is
(a) 4 1 (b) 4 3 (c) 2 1 (d) 1
146. A ball strikes a frictionless horizontal floor at an angle = 450. The coefficient of restitution between the ball and the floor is
2 1
e . The fraction of its kinetic energy lost in collision is
(a) 5/8 (b) 3/8 (c) 3/4 (d) 1/4
147. A smooth rubber cord of length l with spring constant k is suspended from O. The other end is fitted with a bob B. A small sleeve of mass m starts falling from O. Neglecting the masses of the cord and bob find the maximum elongation of the cord. (a) mg kl k mg 2 1 1 (b) mg kl k mg 2 1 A O B (c) k mg (d) mg k k mg 1
148. A force acts on a mass of 40 kg and changes its velocity from 3 m/s to 12 m/s then the impulse of the force is
(a) 360 N-s (b) 36 N-s (c) 600 N-s (d) none of these
149. A shell fired along a parabolic path explodes into two fragments of equal mass at the top of the trajectory. One of the fragments returns to the point of firing having retracted its original path. If v is the velocity of projectile at the highest point, then three statements are given as below
(i) after explosion, the other fragment moves with 2v along +x-axis
(ii) after explosion both fragments reach the ground with separation 2R between them (iii) after explosion, both fragments hit the ground simultaneously at
v R t
(a) only (i) is correct (b) only (ii) is correct
(c) both (ii) and (iii) are correct (d) both (i) and (iii) are correct
150. In the shown diagram mA mB = 1 kg, spring constant
= 200 N/m. InitiallyvB 2m/s,vA 0. Find the maximum
compression produced in the spring. (Neglect friction)
B A
2 m/s
(a) 20 cm (b) 10 cm (c) 5 cm (d) 15 cm
151. A ball falls from a height on a horizontal surface. If the collision is elastic, the graph between speed (v) and time (t) upto the second collision looks like
t v (a) t v (b) t v (c) t v (d)
152. A ball is moving with velocity 2 m/s towards a heavy wall moving towards the ball with speed 1 m/s as shown. Assuming collision to be elastic find the velocity of ball immediately after the collision
1 m/s 2 m/s
(a) 2 m/s (b) 1 m/s (c) 3 m/s (d) 4 m/s
153. A disc of mass 0.1 kg is kept floating horizontally in mid air by firing bullets of mass 0.05 kg each vertically at it, at the rate of 10 bullets per second. If the bullets rebound with the same speed, what is the speed of the bullets with which these are fired? (g = 10 m/s2) (a) 10 m/s (b) 1 m/s (c) 0.1 m/s (d) 0.01 m/s
154. A heavy steel ball of mass greater than 1 kg moving with a speed of 2m sec–1collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed
(a) 2 m sec–1 (b) 4 m sec–1 (c) 2 × 104m sec–1 (d) 2 × 103m sec–1 155. A body of mass ‘M’ collides against a wall with a velocity v and retraces its path with the
same speed. The change in momentum is (take initial direction of velocity as positive)
(a) zero (b) –2 Mv (c) Mv (d) 4 Mv
156. A gun fires a bullet of mass 50 gm with a velocity of 30 m sec–1. Because of this the gun is pushed back with a velocity of 1 m sec–1. The mass of the gun is
(a) 15 kg (b) 30 kg (c) 1.5 kg (d) 20 kg
157. A metal ball falls from a height of 32 metre on a steel plate. If the coefficient of restitution is 0.5, to what height will the ball rise after second bounce?
(a) 2 m (b) 4 m (c) 8 m (d) 16 m
158. At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two position vectors connecting point of explosion to fragments to make 90° is
159. A body of mass m1 moving with a velocity 3 ms1 collides with another body at rest of
mass m2. After collision the velocities of the two bodies are 2 ms–1and 5 ms–1respectively along the direction of motion of m1. The ratio m1/ m2 is
(a) 12 5 (b) 5 (c) 5 1 (d) 5 12
160. 100 g of iron ball having velocity 10 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the ball is
(a) 100 N (b) 10 N (c) 0.1 N (d) 1.0 N
161. An impulse J is applied on a ring of mass m along a line passing through its centre O and parallel to horizontal surface. The ring is placed on a rough horizontal surface. The linear velocity of centre of ring when it starts rolling without slipping is
O
O J
(a) J/m (b) J/2m (c) J/4m (d) J/3m
162. Ball 1 collides with an another identical ball 2 at rest as shown in figure. For what value of coefficient of restitution e, the velocity of second ball becomes two times that of 1 after collision
1
2
(a) 1/3 (b) 1/2 (c) 1/4 (d) 1/6
163. A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. After collision big ball obtains velocity v. Then what is the value of v (e = 1)
(a) u m M m M (b) u m M m (c) M m u m 2 (d) u m M M
164. A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity
(a) v/2 (b) 2 v (c) v/ 2 (d) v
165. A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system
(a) Momentum is m M mvM (b) Kinetic energy is 2 2 mv (c) Momentum is M m M mv( ) (d) Kinetic energy is ) ( 2 2 2 m M v m
166. A metal ball of mass 2 kg moving with a velocity of 36 km/h has an head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is
(a) 40 J (b) 60 J (c) 100 J (d) 140 J
167. Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends, what would be its angular velocity?
L
M J=MV M
(a) V/L (b) 2V/L (c) V/3L (d) V/4L
168. In the figure shown, the position-time graph of a particle of mass 0.1 Kg is shown. The momentum at t 2secis (a) 0.2 kg m sec–1 (b) – 0.2 kg m sec–1
(c) 0.1 kg m sec–1 (d) – 0.4 kg m sec–1 2 4 6 t (sec) 2 4 6 x (m)
169. The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to 8 second will be (shown geometry is semicircular)
(a) – 4N-s (b) + 4 N-s (c) 6 N-s (d) Zero –2 4 +2 4 2 6 8 Time (s) F or ce ( N )
170. A bullet emerges from the muzzle of a gun with a velocity of 300 m/sec. The resultant force on the bullet when it is in the gun barrel is given byF t
3 10 4 400 5
. Assuming the force becomes zero at the end of the barrel, find the impulse of the force and mass of bullet. (a) 0.6 N-s and 2 gm (b) 1.2 N-s and 5 gm
(c) 12 N-s and 5 gm (d) 2.4 N-s and 2 gm 171. A particle of mass m moving with velocity u makes an
elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to
F0linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F is0
(a) mu/T (b) 2mu/T
(c) mu/2T (d) None of these
T/2 T t
F0
F
172. A smooth sphere is moving on a horizontal surface with velocity vector 2iˆ2jˆimmediately
before it hits a frictonless vertical wall. The wall is parallel to jˆ vector and the coefficient of restitution between the sphere and the wall is
2 1
e . The velocity vector of the sphere after
it hits the wall is
(a) iˆ jˆ (b) iˆ 2jˆ (c) iˆ jˆ (d) 2iˆ jˆ
173. The variation of momentum with time of one of the body in a two body collision is shown in figure. The instantaneous force is maximum corresponding to point
(a) P (b) Q
(c) R (d) none of these t
P
P RQ
174. Two particles of mass m and 2m, moving in opposite directions collide elastically with velocities v and 2v. Their velocities after collision are respectively.
(a) 0, 3v (b) 3v, 0 (c) 2v, 0 (d) v, 2v 175. Consider the following two statements
(B) Kinetic energy of system of particles is zero (a) A implies B and B implies A
(b) A does not imply B and B does not imply A (c) A implies B but B does not imply A
(d) B implies A but A does not imply B
176. Two identical discs are moving with the same kinetic energy. One rolls and the other slides. The ratio of their speed is
(a) 1 : 1 (b) 2: 3 (c) 2 : 3 (d) 1 : 2
177. A disc of mass m and radius r rests on an inclined surface and is supported by a rope that is tangent to the disc and parallel to the inclined surface as shown in the figure. The minimum value of coefficient of static friction, in terms of , that will prevent the disc from slipping down the inclined surface is
(a) tan 5 2 (b) 2 tan (c) tan 3 2 (d) tan
r m178. A sphere which is rotating about its own axis is gently lowered down on to a smooth inclined surface making on angle with the horizontal. The initial angular velocity of rotation is . The translational velocity when it
reaches the horizontal surface is
R
L
(a) 2gLtan (b) tan
7 10 gL (c) 7 tan 10 22R2 gL (d) none of these
179. A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass
(a) of the box remains constant
(b) of the box plus the ball system remains constant (c) of the ball remains constant
(d) of the ball relative to the box remains constant
180. All the particles of a body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is
(a) = R (b) R (c) > R (d) R
181. A spherical shell first rolls and then slips down an inclined plane. The ratio of its acceleration in two cases will be
182. Three uniform rods, each of length 2l and mass m are attached (end to end) to form a triangular frame work. The moment of inertia of the frame work about an axis passing through the midpoints of two of its sides is
(a) 2 4 1 ml (b) 2 2 1 ml (c) 2 4 3 ml (d) 2 4 5 ml
183. The moment of inertia of a ring about its geometrical axis is I, then its moment of inertia about its diameter will be
(a) 2 I (b) I/2 (c) I (d) l/4
184. A Yo-Yo is placed on a rough horizontal surface and a constant force F pulls it vertically, which is less then its weight. Then
(a) it will move towards left (b) it will move towards right
(c) the friction force acts towards left (d) both (a) and (c) are true
F
C O
185. The angular momentum and the moment of the inertia are respectively (a) vector and tensor quantities (b) scalar and vector quantities (c) scalar and scalar quantities (d) vector and vector quantities
186. The kinetic energy of rotation of particle is 18 joule. If the angular momentum vector coincides with the axis of rotation and the moment of inertia of the particle about this axis is 0.01 kg-m2, then its angular momentum will be
(a) 0.06 J-sec (b) 0. 6 J-sec (c) 0.006 J-sec (d) zero
187. The point with position vector r1 is the centre of mass of a set of particles each of mass m
while the point with position vector r2 is the centre of mass of a second set of particles
each of mass (m). The position vector r for the centre of mass of the combined set of all the masses will be given by
(a)
2 2 1 r r r (b)
1 2 1 r r r (c) 2 1 2 1 ` r r r r r (d) 1 2 1 r r r 188. A small ring is free to move on a smooth wire bent in the form of a vertical circular loop of radius r. The loop is rotating with constant angular velocity about the vertical diameter while the ring remains at rest relative to wire at a distance
2
r from the axis. The angular velocity
of ring is equal to (a) r g 2 (b) 3 2 r g (c) r g 3 (d) r g 2 3
189. A beam is supported at its centre on a fulcrum and forces acts as shown. The force F for the beam to be in equilibrium is (a) 67 N (b) 12 N (c) 46.26 N (d) 35 N 12N F 23N 23 mm 80 mm 100 mm
190. A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a rough surface (floor). The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. The horizontal velocity of the axis of cylindrical part of the carpet when its radius reduces to
2 R is (a) 2 9gR (b) 3 14gR (c) gR 5 2 (d) gR 4 1
191. Two spherical bodies of masses M and 5 M and radii R and 2R respectively are released in free space with their initial separation between their centres equal to 12R. Then the distance covered by the smaller body just before collisions is
(a) 7.5 R (b) 1.5 R (c) 2.5 R (d) 4.5 R
192. A force of 15 N is applied to a spanner at an effective length of 140 mm from the centre of a nut. The magnitude of the force required to produce the same moment if the effective length is reduced to 100 mm is
(a) 2.1 N (b) 21 N (c) 15 N (d) 0 N
193. A rectangular block has a square base measuring a a and its height is h. It moves on a horizontal surface in a direction perpendicular to one of the edges. The coefficient of friction is . It will topple if
(a) a h (b) h a 2 (c) h a (d) h a 2
194. A particle of mass 2 kg is moving with uniform velocity along the line 2 3 x
y in the XY
plane. X-component of its velocity is 15 m/sec. Angular momentum (magnitude) of the particle about the point
m 3 1 m, 1 is
(a) 60 kg m2/sec (b) 40 kg m2/sec (c) zero (d) 30 3kg m2/sec 195. A solid sphere, starting from rest, rolls down (without slipping) an inclined plane of length s
and inclination . Its speed when it reaches the bottom of the plane is (a) 2gssin (b) sin
3 4 gs (c) sin 9 16 gs (d) sin 7 10 gs
