LEVEL – I

Q:1. When a body is stationary:

(A) There is no force acting on it

(B) The forces acting on it are not in a contact with it

(C) The combination of forces acting on it balance each other

(D) The body is in vacuum

Q:2. A toy train consists of three identical compartments X, Y and Z. It is pulled by a constant horizontal force F applied on Z horizontally. Assuming there is negligible friction, the ratio of tension in string connecting XY and YZ is:

(A) 2:1

(B) 3:2

(C) 1:2

(D) 2:3

Q:3. Two blocks of masses 2 kg and 1 kg are in contact with each other on a frictionless table, when a horizontal force of 3.0 N is applied to the block of mass 2 kg the value of the force of contact between the two blocks is:

(A) 4 N

(B) 3 N

(C) 2 N

(D) 1 N

Q:4. A block of metal weighing 2 Kg is resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1 Kg/sec and at a speed of 5m/sec. The initial acceleration of the block will be:

(A) 2.5 m/sec^{2}

(B) 5.0 m/sec^{2}

(C) 10 m/sec^{2}

(D) none of above

Q:5. When a force of constant magnitude always act perpendicular to the motion of a particle then:

(A) Velocity is constant

(B) Acceleration is constant

(C) KE is constant

(D) None of these

Q:6. Two masses M_{1} and M_{2} are attached to the ends of string which passes over the pulley attached to the top of a double inclined plane. The angles of inclination of the inclined planes are α and β . Take g = 10 ms^{-2}. If M_{1} = M_{2} and α = β , what is the acceleration of the system ?

(A) zero

(B) 2.5 ms^{-2}

(C) 5 ms^{-2}

(D) 10 ms^{-2}

Q:7. Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is:

(A) 0.33

(B) 0.25

(C) 0.75

(D) 0.80

Q:8. A trolley car slides down a smooth inclined plane of angle of inclination θ. If a body is suspended from the roof of the trolley car by an inextensible string of length l, the corresponding tension in the string will be

(A) mg

(B) mg cosθ

(C) mg sinθ

(D) None of these

Q:9. A block of mass m is held at the top of an inclined rough plane of angle of inclination θ . The coefficients of static and kinetic friction are μ_{1} and μ_{2} respectively. If the block is pushed down at the verge of slipping, assuming θ < tan^{-1} μ_{1} , Its acceleration down the plane is :

(A) g[Sin θ – μ_{1} Cos θ]

(B) g[Sin θ – μ_{2} Cos θ]

(C) g( Sin θ – μ_{1} Cos θ]

(D) g

Q:10. A satellite in force-free space sweeps stationary interplanetary dust at a rate (dM/dt) = αv . The acceleration of satellite is:

(A) -2v^{2}/M

(B) -αv^{2}/M

(C) -αv^{2}/2M

(D) -αv^{2}

__ANSWER:__

1. (C) 2. (C) 3. (D) 4. (A) 5. (C) 6. (A) 7. (C) 8. (B) 9. (B) 10. (B)

LEVEL – I

Q:11. Three blocks are connected on a horizontal frictionless table by two light strings, one between m_{1} and m_{2}, another between m_{2} and m_{3} . The tensions are T1 between m1 and m2 and T_{2} between m_{2} and m_{3} . if m_{1} = 1 kg , m_{2} = 8 kg, m_{3} = 27 kg and F = 36 N applied on m_{3} , then T_{2} will be

(A) 18 N

(B) 9 N

(C) 3.375 N

(D) 1.75 N

Q:12. A force-time graph for the motion of a body is shown in figure.

Change in linear momentum between 0 and 8 s is:

(A) Zero

(B) 4 N-s

(C) 8 Ns

(D) None

Q:13. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force F is applied at one end of the rope, the force which the rope exerts on the block is:

(A) F/(M+m)

(B) F

(C) FM/(m+M)

(D) 0

Q:14. A chain of length L and mass M is hanging by fixing its upper end to a rigid support. The tension in the chain at a distance x from the rigid support is:

(A) Zero

(B) F

(C) Mg(L-x)/L

(D) Mg(L-x)/M

Q:15. Two masses m and m’ are tied with a thread passing over a pulley, m’ is on a frictionless horizontal surface and m is hanging freely. If acceleration due to gravity is g, the acceleration of m’ in this arrangement will be

(A) g

(B) g/(m+ m’)

(C) g/m’

(D) g/(m- m’)

Q:16. A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction the block and the wall is 0.5, the magnitude of the frictional force acting on the block is:

(A) 2.5 N

(B) 0.98 N

(C) 4.9 N

(D) 0.49 N

Q: 17. A block A of mass 2 kg rests on another block B of mass 8 kg which rests on a horizontal floor. The coefficient of friction between A and B is 0.2 while that between B and floor is 0.5. When a horizontal force of 25 N is applied on the block B. The force of friction between A and B is:

(A) Zero

(B) 3.9 N

(C) 5.0 N

(D) 49 N

Q:18. A ball weighing 10 gm hits a hard vertical surface with a speed of 5m/s and rebounds with the same speed. The ball remains in contact with the surface for (0.01) sec. The average force exerted by the surface on the ball is:

(A) 100 N

(B) 10 N

(C) 1 N

(D) 0.1 N

Q:19. Two masses A and B each of mass M are fixed together by a massless spring. A force F acts on the mass B as shown in figure.

At the instant shown the mass A has acceleration a. What is the acceleration of mass B?

(A) (F/M)-a

(B) a

(C) -a

(D) (F/M)

Q:20. An object is placed on the surface of a smooth inclined plane of inclination θ. It takes time t to reach the bottom. If the same objective is allowed to slide down a rough inclined plane of same inclination θ , it takes nt to reach the bottom where n is a number greater than 1. The coefficient of friction μ is given by

(A) μ = tan (1-1/n^{2})

(B) μ = cot (1-1/n^{2})

(C) μ = tan (1-1/n^{2})^{1/2}

(D) μ = cot (1-1/n^{2})^{1/2}

__ANSWER:__

11. (B) 12. (B) 13. (C) 14. (C) 15. (B) 16. (B) 17. (B) 18. (B) 19. (A) 20. (A)