Kinematics Assignment

Kinematics, Forces

1. A bird flies for 4 s with a velocity of t 2 m/s in a straight line, where t = time in seconds. It covers a distance of

(a) 2 m (b) 4 m (c) 6 m (d) 8 m

2. A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction.

(a) due north (b) 30°east of north

(c) 30° west of north (d) 60° east of north

3. A particle has an initial velocity of 9 m/s due east and a constant acceleration of 2 m/s2 _due west. The distance covered by the particle in the fifth second of its motion is

(a) 0 (b) 0.5 m (c) 2 m (d) none of these

4. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

(a) 12

t (b) t34 (c) t32 (d) t2

5. Water drops fall at regular intervals from a roof. At an instant when a drop is about to leave the roof, the separations between 3 successive drops below the roof are in the ratio

(a) 1 : 2 : 3 (b) 1 : 4 : 9 (c) 1 : 3 : 5 (d) 1 : 5 : 13

6. A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is:

(a) MgL (b) MgL/3 (c) MgL/9 (d) MgL/18

7. Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown straight up, B is thrown straight down and C is thrown horizontally. They hit the ground with speeds v_Av_B and v respectively. ThenC

(a) v_A v_Bv_C (b) v_Bv_C v_A (c) v_A v_Bv_C (d) v_A v_Bv_C

8. A boat which has a speed of 5 km/h 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 kilometers per hour is

(a) 1 (b) 3 (c) 4 (d) ₄₁

9. A projectile is moving at 60 m/s at its highest point, where it breaks into two equal parts due to an internal explosion. One part moves vertically up at 50 m/s with respect to the ground. The other part will move at

(a) 110 m/s (b) 120 m/s (c) 130 m/s (d) 10 61m/s 10. A particle thrown up vertically reaches its highest point in time t₁ and returns to the ground

in further t₂. The air resistance exerts a constant force on the particle opposite to its direction of motion.

(a) t₁ > t₂ (b) t₁ = t₂ (c) t₁ < t₂

(d) may be (a) or (c) depending on the ratio of the force of air resistance to the weight of the particle.

11. Two particles are projected simultaneously in the same vertical plane, from the same point, but with different speeds and at different angles with the horizontal. The path followed by one, as seen by the other, is

(a) a vertical straight line

(b) a straight line making a constant angle (90) with the horizontal (c) a parabola (d) a hyperbola

12. A car is moving in a circular horizontal track of radius 10m 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 the track is

(a) zero (b) 30° (c) 45° (d) 60°

13. Two particles are projected simultaneously in the same vertical plane from the same point, with different speedsu and ₁ u , making angles ₂  and ₁  respectively with the horizontal,₂ such that u₁cos₁u₂cos_2. The path followed by one, as seen by the other (as long as both are in flight), is

(a) a horizontal straight line (b) a vertical straight line

(c) a parabola (d) a straight line making an angle 12 with the horizontal

14. A particle moves along the positive branch of the curve 2 x y 2  where ,x 2 t x 2  and y are measured in metres and t in seconds. At t = 2s, the velocity of the particle is

(a) _{2 iˆ 4jˆm s} (b) _{4 iˆ 2jˆm s} (c) _{2 iˆ 4jˆm s} (d) _{4 iˆ 2jˆm s}

15. A steel ball strikes a fixed horizontal steel plate at an angle  with the vertical. If the coefficient of restitution is e, the angle at which the rebound will take place is

(a)  (b) _        e tan tan 1 (c) etan  (d)         tan e tan 1

16. A light particle moving horizontally with speed of 12 m/s strikes a very heavy block moving in the same direction at 10 m/s. The collision is one-dimensional and elastic. After the collision, the particle will

(a) move at 2 m/s in its original direction (b) move at 8 m/s in its original direction

(c) move at 8 m/s opposite to its original direction (d) move at 12 m/s opposite to its original direction

17. In which of the following cases the centre of mass of a rod is certainly not at its geometrical centre?

(a) The density continuously increases from left to right (b) The density is constant

(c) The density decreases from left to right upto the centre and then increases (d) The density increases from left to right upto the centre and then decreases

12m s

s m 10

18. Two racing cars of masses m and ₁ m are moving in circles of radii 2 r and 1 r respectively,,2

their speeds are such that each of them make a complete circle in the same length of time t. The ratio of the angular speed of the first to the second car is

(a) m₁:m₂ (b) r₁:r₂ (c) _1:1 (d) m₁r₁:m₂r₂

19. A particle of mass m moving with velocity u makes an elas-tic one-dimensional collision with a stationary parelas-ticle of mass m. They are in contact for a very brief time T. Their force of interaction increases from zero to F linearly in₀ 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

20. A particle is falling freely under the gravity over a short distance from P to Q. M is the mid point of PQ. Then

(a) its kinetic energy at Q will be double than at M

(b) the time of motion from P to Q will be less than 1.5 times the time of the motion from P to M

(c) its velocity at Q will be double its velocity at M

(d) its average velocity from P to Q is double its average velocity from P to M

21. A motor car is travelling at 60 m/s on a circular road of radius 1200m. It increases its speed at the rate of 2

s m

4 . The acceleration of the car is (a) 3 2 s m (b) 4 2 s m (c) 5 2 s m (d) 7 2 s m

22. A particle strikes a horizontal frictionless floor with a speed u, at an angle  with the verti-cal, and rebounds with a speed v, at angle  with the vertical. The coefficient of restitution between the particle and the floor is e. The magnitude of v is

(a) eu (b) (1 – e)u (c) 2_ 2 2_ cos e sin u (d) 2 2_ 2_ cos sin e u

23. A particle moves with a velocity 5iˆ3jˆ6kˆms under the influence of a constant force

. N kˆ 20 jˆ 10 iˆ 10

F   The instantaneous power applied to the particle is

(a) 200 J/s (b) 40 J/s (c) 140 J/s (d) 170 J/s

24. Three blocks 1, 2 and 3 each of mass m are arranged as shown in the figure. If the blocks were released from rest and the ratio of accel-eration of the blocks 1 and 3



a₁ a₃



is 2. Then the ratio of accelera-tion of the blocks 2 and 3



a₂ a₃



is

(a) 2 (b) 2.5 (c) 1 (d) 1.5 2 1 3 0 F 2 T  t F T    u v

25. A particle of mass m makes an elastic, one-dimensional collision with a stationary particle₁ of mass m . What fraction of the kinetic energy of ₂ m is carried away by ₁ m ?₂

(a) 2 1 m m (b) 1 2 m m (c)

_

_

2 2 1 2 1 m m m m 2  (d)



1 2



2 2 1 m m m m 4 

26 A particle of mass attached to a string of length l is describing circular motion on a plane inclined at angle  with the horizontal. For the particle to reach the highest point, its velocity at the lowest point must exceed

(a) 5 g sin (b) 5g

(c) (5/2)g (d) (5/2)gsin

27. A disc of mass m and radius R has a concentric hole of radius r. Its moment of inertia about an axis through its centre and perpendicular to its plane is

(a) m(R r)2 2 1  (b) m(R r ) 2 1 2_ 2 (c) m(R r)2 2 1  (d) m(R r ) 2 1 2_ 2

28. A particle of small mass m is joined to a very heavy body by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

(a) mg (b) 2 mg (c) 4 mg (d) >> mg

29. A smooth ball of mass m moving with the velocity v makes₀ an elastic impact on another smooth ball of mass M at rest. After impact the velocity components v and ₁ v of the balls₂ are

(a) v₀cos,0 (b) v₀sin,0 (c) v0sin,v0sin (d) none of these

30. The coefficient of friction between the block A of mass m and triangular wedge B of mass M is  . There is no friction between the wedge and the plane. If the system (block A + wedge B) is released so that there is no sliding between A and B. The inclination  is

(a) tan1 (b)           M m tan 2 1 1 (c)  cos

 

2 2 1 1 (d)  sin

 

2 2 1 1

31. In the figure, the blocks A, B and C of mass m each have acceleration a₁,a₂ and a respectively..₃

1

F and F are external forces of magnitudes 2mg2

and mg respectively. (a) a₁a₂a₃ (b) a₁a₃a₂ (c) a₁a₂,a₂ a₃ (d) a₁a₂,a₂a₃ m M ) A B   1 v 2 v  ) m M 0 v B    m m m m A C mg 2 F₁ 2m F₂ 1mg

32. Two particles A and B are projected simultaneously from a point situated on horizontal plane. The particle A is projected vertically up with velocity V while the particle B is_A projected up at angle 30° above horizontal with velocity V . After 5 sec the particles were_B observed moving mutually perpendicular to each other. The velocity of projection of the particle V and _A V respectively are_B

(a) 1

ms

50  ,50ms1 (b) 100ms1,50ms1 (c) V can have any value,_A 1

ms

100  (d) none of these

33. The displacement of a particle varies with time asy(6sint8sin3t)cm,then its maxi-mum acceleration is

(a) 2

18 (b) 62 (c) 22 (d) 22 g

34. In the figure, the vertical sections of the string are long. A is released from rest from the position shown.

(a) The system will remain in equilibrium

(b) The central block will move down continuously (c) The central block will undergo SHM

(d) The central block will undergo periodic motion but not SHM

35. A block of mass m = 0.1 kg is released from a height of 4m on a curved smooth surface. On the horizontal surface path AB is smooth and path BC offers coefficient of friction 0.1. If the impact of block with the vertical wall at C be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be (take g = 10 ms2)

(a) 29 m (b) 49 m (c) 59 m (d) 109 m

36. A bicycle moves on a horizontal road with some acceleration. The force of friction between the road and the front and rear wheels are F₁ and F₂ respectively.

(a) Both F₁ and F₂ act in the forward direction (b) Both F₁ and F₂ act in the reverse direction

(c) F₁ acts in the forward direction, F₂ act in the reverse direction (d) F₂ acts in the forward direction, F₁ act in the reverse direction

37. A man of mass m = 60 kg is standing on weighing machine fixed on a triangular wedge of angle 60 as shown in the figure. The wedge is moving up with an

upward acceleration _{a 2m s}2 _{. The weight registered by machine is}

(a) 600 N (b) 1440 N

(c) 360 N (d) 240 N

38. In gravity-free space, a man of mass M standing at a height h above the floor throws a ball of mass m straight down with a speed u. When the ball reaches the floor, the distance of the man above the floor will be

(a)        M m 1 h _(b)        M m 2 h (c) 2h (d) a function of m, M, h and u   A B _C m 1 2m m 4 (  a   m m m 2 . 1 A

39. A bullet makes n turns inside the barrel of length l of a rifle and emerges from it with a speed V. Assuming that the bullet moves inside the barrel with a uniform acceleration, the angular velocity of the bullet about its latitudinal axis as it emerges from the barrel is

(a) l v (b) l nv 2 (c) v 2 n  (d) none of these

40. A particle is projected vertically upward with initial velocity 1

ms

25  . During third second of its motion, which of the following statement is correct

(a) displacement of the particle is 30 m (b) distance covered by the particle is 30 m

(c) distance covered by the particle is 2.5 m (d) none of these

41 In a tug-of-war contest, two men pull on a horizontal rope from opposite sides. The winner will be the man who

(a) exerts greater force on the rope (b) exerts greater force on the ground (c) exerts a force on the rope which is greater than the tension in the rope

(d) makes a smaller angle with the vertical

42. A truck moving on horizontal road towards east with velocity 1

ms

20  collides elastically with a light ball moving with velocity 1

ms

25  along west. The velocity of the ball just after collision.

(a) 65ms1 towards east (b) _45ms1 _{towards west}

(c) 65ms1 towards west (d) 1

ms

45  towards east

43. A particle is projected from point P with velocity 1

ms 2

5  perpen-dicular to the surface of a hollow right angle cone whose axis is vertical. It collides at Q normally. The time of the flight of the particle is

(a) 1 sec (b) _{2 sec}

(c) 2 2 sec (d) 2 sec

44. In the arrangement shown, the pulleys are fixed and ideal, the strings are light, m ₁ m₂, and S is a spring balance which is itself massless. The reading of S (in units of mass) is

(a) m 1 m2 (b)



m1 m2



2 1  (c) 2 1 2 1 m m m m  (d) _{1 2} 2 1 m m m m 2 

45. A man holds a ball of mass kg 2 1

in his hand. He throws it vertically upward. During this process his hand moves up by 40 cm and the ball leaves his hand with an upward velocity of

1

ms

4  . The force with which the man pushes the ball is

(a) 5.1 N (b) 10N (c) 14.9N (d) 7N P Q  90 y s 1 m 2 m

46. A bead of mass ‘m’ is released from rest at A to move along the fixed smooth circular track as shown in figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point P described by the angle ₀ ' ' (0) would

(a) increase with  (b) decrease with 

(c) remains constant (d) first increase with  then decrease

47. In the figure, the ball A is released from rest when the spring is at its natural (unstretched) length.For the block B, of mass M to leave contact with the ground at some stage, the minimum mass of A must be

(a) 2M (b) M

(c) 2 M

(d) a function of M and the force constant of the spring

48. A stone tied to string of length L is whirled in a vertical circle, with the other end of the string at 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 its velocity as it reaches a position where the string is horizontal is

(a) _u2_{2gL (b) 2gL}

(c) _u2 _gL

 (d) 2



u2gL



49. A car starts from rest and moves on a surface in which the coefficient of friction between the road and the tyres increases linearly with distance (x). The car moves with the maximum possible acceleration. The kinetic energy (E) of the car will depend on x as

(a) ₂ x 1 E  _(b) x 1 E  (c) _{E x} (d) _{E x}2

50. A force Fk



yiˆxjˆ



, where k is a positive constant, acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0), and then parallel to the y-axis to the point (a, a). The total work done by the force on the particle is

(a) 2

ka 2

 (b) 2ka2 (c) ka2 (d) ka2

51. A spring, which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is W and in the second case₁ is W₂

(a) W ₁ W₂ (b) W ₂ 2W₁ (c) W ₂ 3W₁ (d) W ₂ 4W₁

52. 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 1 e 1 t _(b)







1 e



e 1 t   (c) e2t (d) e°t

53. Two bodies with kinetic energies in the ratio 4 : 1 are moving with equal momentum. The ratio of their masses is

(a) 4 : 1 (b) 1 : 1 (c) 1 : 2 (d) 1 : 4   R 0 P  M B A

54. A body takes n times as much time to slide down a 45° incline as it takes to slide down a smooth 45° incline of identical height. The coefficient of friction is

(a) _n2 1 1  _(b) 2 n 1 1  (c) 2 n / 1 (d) _{1 n}2 1 

55. A boy is sitting on a weighing box placed on a table. The weight of the boy is found to be 30kg. The table along with the weighing box and the boy is thrown up by some mechanism. The weight of the boy during the flight will be found to be

(a) more than 30 kg during ascent and less than 30 kg during descent (b) remain 30 kg throughout the flight

(c) 30 kg at the highest point and zero during ascent and descent (d) zero throughout the flight

56. A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the times of flight in two cases then,

(a) 2 2 1t R t  (b) t₁t₂R (c) R 1 t t1 2 (d) 1 2 2 R 1 t t 

57. A projectile of mass m is projected at an angle  to the horizontal with a velocity v. The instantaneous power of gravity after time t is

(a) mg(gtvsin) (b) 2 2 t mg (c) mg(vcosgt) (d) mg2t2 2 1

58 A boat man A notices a log of wood B floating in a river flowing at a speed v straight across. (a) he should row at some angle other than 90° to the

shore to catch the wood

(b) whether he can catch depends upon the distance of the log from the shore

(c) he should row at an angle 90° to the shore (d) he cannot catch the log of wood at all

59. Under the action of a force, a 2 kg body moves such that its position x as a function of time is given by xt3 3, where x is in meters and t in seconds. The work done by the force in the first two seconds is

(a) 1600 J (b) 160 J (c) 16 J (d) 1.6 J

60. In the figure, the block A of mass m is placed on the block B of mass 2m. B rests on the floor. The coefficient of friction between A and B as well as that between the floor and B is  . Both blocks are given the same initial velocity to the right. The acceleration of A with respect to B is

(a) zero (b)  to the leftg

(c)  to the rightg (d) g 2 1

 to the right

61. A force F acting on a body depends on its displacement x as Fxn. The power delivered by F will be independent of x if n is (a) 1/3 (b) –1/3 (c) 1/2 (d) –1/2   m m 2 A B B A v

62. A spaceship orbits the earth at a constant speed along a circular path. When an astronaut inside the spaceship releases an object, it does not move away from him. Which of the following is the most accurate reason for this?

(a) The astronaut and the object move along the same circular path due to the earth’s gravi tational pull.

(b) An object moving in a circular path round the earth experiences no gravitational pull. (c) The gravitational forces on the object due to the spaceship exactly balance the gravita

tional pull on it due the earth.

(d) The gravitational pull on the object due to the earth is very weak at a large distance from the earth

63. A wedge of height h is released from rest with a light particle P placed on it as shown. The wedge slides down an incline which makes an angle  with the horizontal. All the surfaces are without friction. P will reach the surface of the incline in time

(a) 2_ sin g h 2 (b) _{gsin cos. } h 2 (c) _gtan h 2 (d) _gcos2_ h 2

64. A ship X moving due north with a velocity v observes that another ship Y is moving due west with velocity v. The actual velocity of Y is

(a) v due east (b) _{2 towards northwestv}

(c) v towards southeast (d) _{2 towards northeastv}

65. In the arrangement shown, all surfaces are friction-less. The rod R is constrained to move vertically. The vertical acceleration of R is a and the horizontal ac-₁ celeration of the wedge W is a . The ratio ₂ a1 a2 is

equal to

(a) tan (b) cot (c) sin (d) cos

66. A small ball rolls off the top landing of a staircase. It strikes the midpoint of the first step and then the midpoint of the second step. The steps are smooth, and identical in height and width. The coefficient of restitution between the ball and the first step is

(a) 1 (b) 3/4 (c) 1/2 (d) 1/4

67. In the arrangement shown in the figure, there is friction only between the light string and the sharp spike at the point P. When the blocks are in motion, the tensions in the vertical and horizon-tal sections of the string are 4 N and 3N respectively. The coef-ficient of friction between the string and the spike is equal to

(a) 0.1 (b) 0.2 (c) 0.5 (d) 1

68. A simple pendulum has a string of length l and bob of mass m. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is

(a) 3mg (b) 4mg (c) 5mg (d) 6mg )  P h R  W )

69. In the previous question, when the string is horizontal, the net force on the bob is

(a) mg (b) 3mg (c) _{10 mg} (d) 4mg

70. In a simple pendulum, the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle  with the vertical. The angle  is given by

(a) cos1

_

1/3

_

(b) _60 (c) cos1

_

2/3

_

(d) _0

71. 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 the other end of the spring with an angular velocity  , in gravity-free space. The increase in length of the spring will be

(a) k l m2 (b) ₂ 2 m k l m    (c) ₂ 2 m k l m    (d) none of these

72. A body moves along an uneven horizontal road surface with constant speed at all points. The normal reaction of the road on the body is

(a) maximum at A (b) maximum at B

(c) minimum at C (d) the same at A, B and C

73. The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross-section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

(a) always be in contact with the inner wall of the tube (b) always be in contact with the outer wall of the tube

(c) initially be in contact with the inner wall and later with the outer wall (d) initially be in contact with the outer wall and later with the inner wall

74. For a car taking a turn on a horizontal surface, let N and ₁ N be the normal reactions of the2

road on the inner and outer wheels respectively. (a) N is always greater than₁ N₂

(b) N is always greater than ₂ N1

(c) N is always equal to 1 N2

(d) Either (a) or (b) depending on the speed of the car and the radius of curvature of the road

75. A man stands at one end of a boat which is stationary in water. Neglect water resistance. The man now moves to the other end of the boat. The centre of mass of the ‘man plus boat’ system will remain stationary with respect to water

(a) in all cases

(b) only when the man is stationary finally

(c) only if the man moves without acceleration on the boat (d) only if the man and the boat have equal masses

76. A man hangs from a rope attached to a hot-air balloon. The mass of the man is greater than the mass of the balloon and its contents. The system is stationary in air. If the man now

A B C C A _B   k m 

O

 



climbs up to the balloon using the rope, the centre of mass of the ‘man plus balloon’ system will

(a) remain stationary (b) move up

(c) move down (d) first move up and then return to its initial position

77. There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is C , while the centre of mass of the ‘com-₁ partment plus passengers’ system is C . If the passengers move about inside the compart-₂ ment,

(a) both C and ₁ C will move with respect to the ground₂ (b) neither C nor 1 C will move with respect to the ground2

(c) C will move but ₁ C will be stationary with respect to the ground₂ (d) C will move but ₂ C will be stationary with respect to the ground1

78. A ball attached with a string whose other end is fixed at O is released from a horizontal position. The angle made by the string with the vertical when the acceleration vector of the ball is directed horizontally is (a) _tan1 _{2 (b)} 2 1 cos1 _(c) 2 tan1 (d) ₅ 1 cos1

79. In the system shown, the mass m moves in a circular arc of angular amplitude 60°. The minimum value of coefficient of friction between the mass 4 m and the surface of the table to prevent slipping is

(a) 0.25 (b) 0.40

(c) 0.50 (d) none of these

80. Power applied to a particle varies with time as P(3t22t1)W, where t is in second. Find the change in its kinetic energy between time t = 2 s and t = 4s

(a) 32 J (b) 44 J (c) 61 J (d) 102 J

81. A truck weighing 8000 kg is moving along a track with negligible friction at 2 m/s, with the engine turned off when it begins to rain hard. The raindrops fall vertically with respect to the ground at a constant rate of 100 kg/s. The speed of the truck when it has collected 2000 kg of rain is

(a) 1.6 m/s (b) 2.4 m/s (c) 1.4 m/s (d) 1.0 m/s

82. Displacement of a particle in 2 sec, if its initial velocity is (3i4i)m s and acceleration

2 s m ) i 4 i 3 (  is (a) zero (b) 1m (c) 5m (d) 2m

83. A particle is projected with velocity (4i3i)ms. Taking P.E. = 0 at point of projection, the ratio of KE to PE at maximum height is given by

(a) 1 : 1 (b) 16 : 9 (c) 9 : 16 (d) none of these

 m

4

84. Two blocks of mass 10 kg each are placed on a smooth horizontal surface. The blocks are given the velocities in opposite direction as shown in diagram. The maxi-mum compression in the spring is

(a) k 10 (b) k 110 (c) k 125 (d) k 1125

85. A force F(3tiˆ5jˆ)N acts on a body due to which its displacement varies as s(2t2iˆ5jˆ).

Work done by this force in 2 sec is

(a) 23 J (b) 32 J

(c) zero (d) can’t be obtained

86. Choose the wrong statement

(a) in an inelastic collision mechanical energy can’t be conserved (b) in an elastic collision total mechanical energy is conserved

(c) in an elastic collision linear momentum must be conserved in any direction (d) none of these

87. Wedge A and block B moves with horizontal acceleration a. The horizontal plane is smooth and friction coefficient between wedge and block is 0.8. If m = 1 kg and 2

s m 14 a  then frictional force acting on B is (a) 15 N (b) 2 N (c) 9.8 N (d) 11.2 N

88. A projectile is projected with speed u with angle 60° with horizontal from the foot of an incline plane inclined at 30° with horizontal. If projectile hits the incline plane horizontally, then its range on incline plane will be

(a) g 2 u2 (b) g 4 u 3 2 (c) g 2 u 3 2 (d) g u2

89. In the shown figure find the minimum value of  for a constant

velocity of projection so that it passes through point P. Here APC is a semicircle of radius R with centre O.

(a) 30° (b) 45°

(c) cot1(12) (d) tan1(12)

90. A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down it.

(a) gR (b) 2gR (c) 3gR (d) 5gR

91. A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M and sticks to it. If the block rises to a height h, the initial velocity of the block will be

(a) 2gh (b) m gh 2 ) m M (  (c) m M gh 2 m  (d) M gh 2 ) m M (   v A O C P m M A a   B 10 10 s m 5 10m s k

92. A man can swim in still water at a speed of 5 km/hr. He wants to cross a river 600m wide, flowing at the rate o 3km/hr. If he heads in a direction making an angle of 120° with stream direction, then he will reach a point on the other bank (approx)

(a) upstream at a distance of 70 m (b) downstream at a distance of 70 m (c) directly on the other side of the bank (d) never reach the other bank

93. Two blocks A and B having masses 2 kg and 8 kg are arranged as shown in the figure. The pulley P and Q are light and frictionless. The blocks are resting on a horizontal floor. At moment t = 0 a force F = 60 t (N) starts acting on the pulley P along vertically upward direction. The time interval between the blocks A and B to lose contact with ground (Taking g = 10 m/s2_).

(a) 2 sec (b) 1 sec (c) 0.5 sec (d) 1.5 sec

94. A non-zero external force acts on a system of particles. The velocity and acceleration of the centre of mass are found to be v_ and a_ at an instant t . It is possible that

(i) v_ 0,a_ 0 (ii) v_0,a_ 0 (iii) v_ 0,a_ 0 (iv) v_ 0,a_ 0

which of the following choice is correct

(a) (i) (ii) (b) (ii) (iv) (c) (i), (iii) (d) (i), (iv)

95. A block of mass M is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F. The kinetic energy of the block increases 20 J in one second

(a) the tension in the string is Mg (b) the tension in the string is F (c) the work done by tension on the block is 20 J in the above one sec.

(d) the work done by the force of gravity is 20 J in the above one sec.

96. A elastic spring has a length a when the tension in it is 4N. Its length is ‘b’ when the tension is 5N. What is the length when the tension in it is 9N.

(a) 5a + 4b (b) 4a + 5b (c) 5b – 4a (d) 4a – 5b

97. A set of n identical cubical blocks lie at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed V towards the next one at time t = 0, all collisions are elastic and head on. Then

(a) the last block starts moving at

V L ) 1 n ( t 

(b) the last block starts moving at

V 2 L ) 1 n ( t 

(c) the centre of mass of the system will have final speed V (d) the centre of mass of the system will have a final speed V/n

98. Two particles are projected simultaneously from two points O and O such that 10 m is the horizontal and 5 m is the vertical distance between them as shown

in the figure. They are projected at the same inclination 60° to the horizontal with the same velocity 10 m/s. The time after which their separation becomes minimum is

(a) 2.5 sec (b) 1 sec

(c) 5 sec (d) 10 sec B A P Q O m 5 m 10 s m 10 s m 10  60  60 O

99. A ship is travelling due east at 10 km/h. A ship heading 30° east of north is always due north from the first ship. The speed of the second ship in km/h is

(a) _{20 2} (b) 2 3 20 (c) 20 (d) 2 20

100. A train accelerates from rest at constant rate  for distance s₁ and time t₁. After that it retards to rest at constant rate  for distances₂ and time t₂. Which of the following relation is correct ? (a) 2 1 2 1 t t s s     _(b) 2 1 2 1 t t s s     _(c) 1 2 2 1 t t s s     _(d) 1 2 2 1 t t s s    

1.

(b)

2.

(c)

3.

(b)

4.

(c)

5.

(c)

6.

(d)

7.

(a)

8.

(b)

9.

(c)

10.

(c)

11.

(b)

12.

(c)

13.

(a)

14.

(c)

15.

(b)

16.

(b)

17.

(a)

18.

(c)

19.

(b)

20.

(b)

21.

(c)

22.

(c)

23.

(c)

24.

(b)

25.

(d)

26.

(a)

27.

(d)

28.

(b)

29.

(b)

30.

(d)

31.

(b)

32.

(c)

33.

(a)

34.

(d)

35.

(c)

36.

(d)

37.

(c)

38.

(a)

39.

(b)

40.

(c)

41.

(b)

42.

(a)

43.

(a)

44.

(d)

45.

(c)

46.

(c)

47.

(c)

48.

(d)

49.

(d)

50.

(c)

51.

(c)

52.

(b)

53.

(d)

54.

(a)

55.

(d)

56.

(b)

57.

(a)

58.

(c)

59.

(c)

60.

(a)

61.

(b)

62.

(a)

63.

(a)

64.

(b)

65.

(a)

66.

(b)

67.

(b)

68.

(d)

69.

(c)

70.

(c)

71.

(b)

72.

(a)

73.

(c)

74.

(b)

75.

(a)

76.

(a)

77.

(c)

78.

(a)

79.

(c)

80.

(b)

81.

(a)

82.

(a)

83.

(b)

84.

(d)

85.

(b)

86.

(c)

87.

(c)

88.

(c)

89.

(d)

90.

(a)

91.

(b)

92.

(b)

93.

(b)

94.

(b)

95.

(b)

96.

(c)

97.

(d)

98.

(b)

99.

(c)

100.

(b)

Answers