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 ?