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Question

# A heavy but uniform rope of length L is suspended from a ceiling. A particle is dropped from the ceiling. At the same instant, the bottom end is given a jerk. Find the velocity of wave pulse at an instant when particle and pulse are at same level.

A
gL2
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B
gL5
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C
gL3
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D
gL4
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Solution

## The correct option is C √gL3Let after time t from start, pulse meets the particle at distance y from lower end. t=∫y01√gxdx=√4yg Distance travelled by particle in this time is (L−y) u=0;a=g∴S=ut−12gt2 L−y=ut−12g×(√4yg)2 L−y−0−2y=0 L=3y⇒y=L3 vpulse=√gy vpulse=√g⋅L3

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