Title 2.Low of motion (Sub.Q ) E.pdf ✅

displacement of the block A in ground frame in 1s. Wedge Fixed incline B A  Block x y Sol.            2 2 1 sin gsin Q.8 A flexible chain of length L slides off the edge of a frictionless table as in Figure. Initially a length y0 hangs over the edge. y (a) Find the acceleration of the chain as a function of y (b) show that the velocity as the chain becomes completely vertical is v = g(L y / L) 2  0 Q.9 Two block A and B having masses m1 = 1 kg, m2 = 4 kg are arranged as shown in the figure. The pulleys P and Q are light and frictionless. All the blocks are resting on a horizontal floor and the pulleys are held such that strings remains just taut. At moment t = 0, a force F = 30t (N) starts acting on the pulley P along vertically upwards direction as shown in the figure. Calculate Q P B A F = 30t (N) (i) the time when the blocks A and B loose contact with ground. (ii) the velocity of A when B looses contact with ground. (iii) the height raised by A upto this instant. (iv) the work done by the force F upto this instant. Sol. (i) 2 sec (ii) 5 m/s (iii) 5/3 m (iv) 175/6 J Q.10 In the given figure find the velocity and acceleration of B, if instantaneous velocity and acceleration of A are as shown in the figure. A B 1 m/s 2 m/s2 Sol. vB = 0.5 m/s , aB = 1 m/s2  Q.11 Three blocks A, B & C are arranged as shown. Pulleys and strings are ideal. All surfaces are frictionless. If block C is observed moving down along the incline at 1 m/s2 . Find mass of block B, tension in string and accelerations of A, B as the system is released from rest. A 37o B C 3 kg 1 m/s2 6 kg Sol. MB = 15 kg, T = 15 N, aA = 5 m/s2  , aB = 9 m/s2  Q.12 Two trains ‘A’ and ‘B’ are approaching each other on a straight track, the former with a uniform velocity of 25 m/sec and later with 15 m/sec. When they are 225 m apart, brakes are simultaneously applied to both of them. The deceleration given by the brakes to the train ‘B’ increases linearly with time by 0.3 m/sec2 every second, while train ‘A’ is given a uniform deceleration. (a) What must be the minimum deceleration of ‘A’ so that the trains do not collide ? (b) What is the time taken by the trains to stop ?

Q.20 In the figure the tension the diagonal string is 60 N. F1 45o F2 W (a) Find the magnitude of the horizontal force  F1 and  F2 that must be applied to hold the system in the positon shown. (b) What is the weight of the suspended block Sol. (a) 2 60 , (b) 2 60 Q.21 The object in figure weights 40 kg and hangs at rest. Find the tensions in the three cords that hold it. 53o 37o 40 kg 53o 37o T3 T1 T2 Sol. T1 = 240 N, T2 = 400 N Q.22 Find the tension in each cord in figure, if the weight of the suspended block is w. 30o 45o (a) (b) 60o 45o Sol. (a) 0.732 w, 0.896 w (b) 2.732 w, 3.346 w Q.23 Three equal masses are suspended from frictionless pulleys as shown in figure. If the weight w2 in figure is 400 Nt, what must be the values of the weights w1 and w3. w2 w1 w3 53o 37o Sol. 240 N, 320 N Q.24 A chain consisting of five links each with mass 100 gm is lifted vertically with constant acceleration of 2m/s2 . as shown. Find (g = 10 m/s2 ) : (a) the forces acting between adjacent links (b) the force F exerted on the top link by the agent lifting the chain (c) the net force on each link F Sol. (b) F = 6 N (c) 0.2 N Q.25 The monkey B shown in figure is holding on the tail of the monkey A which is climbing on a rope. The masses of are monkeys A and B are 5 kg and 2 kg respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry the monkey B with it ? Take g = 10 m/s2 . A B Sol. between 70 N and 105 N Q.26 At the moment t = 0 the force F = at is applied to a small body of mass m resting on a smooth horizontal plane (a is constant). The permanent direction of this force forms an angle a with the horizontal. Find : (a) the velocity of the body at the moment of its breaking off the plane ; (b) the distance traversed by the body up to this moment. m F  Sol.       2 3 2 3 2 2 6a sin m g cos , s 2a sin mg cos v Q.27 A painter of mass M stand on a platform of mass m and pulls himself up by two ropes which hang over pulley as shown. He pulls each rope with the force F and moves upward with uniform acceleration ‘a’. Find ‘a’