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Question

A ball is dropped from height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is :

A
he2n
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B
e2nh
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C
he2n
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D
hen
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Solution

The correct option is C he2n
Let v0 be the velocity with which the ball strikes the Earth first time and vn after the nth rebound.
The coefficient of restitution is
e=v1v0=v2v1=v3v2=.....=vnvn1
en=v1v0×v2v1×v3v2×.....×vnvn1=vnv0
Here, v0=2gh and vn=2gH
en=2gH2gh=Hh
e2n=HhH=he2n

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