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Q.

A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is 25. After how many collisions the amplitude of vibration will become less than 60°

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a

6

b

3

c

5

d

4

answer is B.

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Detailed Solution

From the relation of restitution hnh0=e2n and hn=h0(1−cos60°)⇒hnh0=1−cos60°=252n⇒1−12=45n⇒12=45nTaking log of both sides we get log1−log2=n(log4−log5)0−0.3010=n(0.6020−0.6990)− 0.3010=−n×0.097⇒n=0.30100.097=3.1≈3
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