Title 2-dynamics-of-a-particle-.pdf ✅

Dynamics of a Particle 1. In the adjoining figure if acceleration of M with respect to ground is a, then, (A) Acceleration of m with respect to M is a (B) Acceleration of m with respect to ground is a sin (α/2) (C) Acceleration of m with respect to ground is a (D) Acceleration of m with respect to ground is a tan α 2. A rectangular block weighing 150 N, is lying on a rough inclined plane with inclination angle 45∘ as shown in the figure. The block is tied up by a horizontal string which has a tension of 50 N to keep the block just in equilibrium, then the coefficient of friction between the block and the inclined surface is : (A) Zero (B) 0.33 (C) 0.5 (D) 0.7 3. A plank is held at an angle α to the horizontal (figure) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. With what acceleration and in what direction, a man of mass m should move so that the plank does not move. (A) gsin α (1 + M m ) up the (B) gsin α (1 + M m ) down the incline (C) 2√3 m/s (D) gsin α (1 + M m ) up the incline 4. For the arrangement shown in figure the coefficient of friction between any two surfaces is 0.5 . Which of the following graphs shows correct variation of frictional force/between the 2 kg block and floor with the applied force F. (Take leftward direction of F as positive) (A) (B)
(C) (D) 5. A rod AB is shown in figure. End A of the rod is hinged on the ground. Block is moving with velocity √3 m/s towards right. The velocity of end B of rod when rod makes an angle of 60∘ with the ground is: (A) √3 m/s (B) 2 m/s (C) 2√3 m/s (D) 3 m/s 6. A trolley C shown in the figure is driven with an acceleration a = 3 m/s 2 . The ratio of acceleration of the bodies A and B of masses 10 kg and 5 kg respectively is: (assume pulleys are massless and friction is absent everywhere) (A) 2: 1 (B) 1: 3 (C) 1: 1 (D) 2: 3 7. In the system shown in figure, all the surfaces are smooth. Rod is moved by external agent with acceleration 9 m/s 2 vertically downwards. Force exerted on the rod by the wedge will be : (A) 120 N (B) 200 N (C) 135/2 N (D) 225/2 N 8. In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all blocks are of cubodial shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M ) in figure 1 and figure 2 are a1 and a2 respectively. Then: Figure : 1
Figure : 2 (A) a1 = a2 ≠ 0 (B) a1 = a2 = 0 (C) a1 > a2 (D) a1 < a2 9. An inclined plane makes an angle 30∘ with the horizontal. A groove (OA) of length 5 m cut, in the plane makes an angle 30∘ with OX. A short smooth cylinder is free to slide down the influence of gravity. The Time taken by the cylinder to reach from A to O is : (g = 10 m/s 2 ) (A) 4s (B) 2s (C) 2s (D) 1s 10. A particle of mass m = 0.1 kg is released from rest from a point A of a wedge of mass M = 2.4 kg free to slide on a frictionless horizontal plane. The particle slides down the smooth face AB of the wedge. When the velocity of the wedge is 0.2 m/s the velocity of the particle in m/s relative to the wedge is : (A) 4.8 (B) 5.77 (C) 7.5 (D) 10 MULTIPLE CORRECT ANSWERS TYPE Each of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 11. In the given figure, a block A rests on a smooth triangular block B and the block B is given an acceleration of a = 2 m/s 2 along the plane. (A) normal force on block A due to block B is m(g − a) (B) acceleration of block A relative to block B is a cos θ (C) If friction is present between block and A and B, the coefficient of friction should be greater than a g cos θ, for no relative motion between A and B (D) If friction is present between block and A and B, the coefficient of friction should be greater than acos θ g−asin θ , for no relative motion between A and B 12. Two blocks each of mass 1 kg are placed as shown. They are connected by a string which passes over a smooth (massless) pulley. There is no friction between m1 and the ground and the coefficient of friction between m1 and m2 is 0.2 . A force F is applied to m2. Which of the following statements is/are correct. (A) The system will be in equilibrium if F < 4 N. (B) If F > 4 N the tension in the string will be 4 N. (C) If F > 4 N the frictional force between the block will be 2 N. (D) If F = 6 N the tension in the string will be 3 N. 13. In the given figure, all surface are frictionless and strings and pulleys are massless, then : (A) acceleration of block B is g/2