Questions

A steel ball of mass 0.5 kg is fastened to a cord 20 cm long and fixed at the far end and is released when the cord is horizontal. At the bottom of its path the ball strikes a 2.5 kg steel block initially at rest on a frictionless surface. The collision is elastic. The speed of the block just after the collision will be.

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a

103ms−1

b

23ms−1

c

5ms−1

d

53ms−1

detailed solution

Correct option is B

Let the ball strike the block with a speed u1. Since the initial speed (speed before collision) of the block = u2 = 0 for the perfectly elastic collision. m1u1=m1v1+m2v2 e=1=u1v2−v1⇒v2−v1=u1Applying conservation of momentum0.5u1=0.5v1+2.5v2u1=−v1+v2⇒v2=u13=2gl3=23 ms−1

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Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block 1 and block 3 have mass m each and block 2 has mass M (M > m). Block 2 and block 3 are initially stationary, while block 1 is initially moving towards block 2 with speed v as shown. Assume that all collisions are head on and perfectly elastic. What value of M/m ensures that block 1 and block 3 have the same final speed?

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