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Question

A small hoop of mass m is given an initial velocity of magnitude v0 on the horizontal circular ring of radius `r'. If the coefficient of kinetic friction is μk the tangential acceleration of the hoop immediately after its release is (assume that horizontal ring to be fixed and not in contact with any supporting surface)

A
μk g
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B
μkv20r
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C
μkg2+v20r
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D
μkg2+v40r2
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Solution

The correct option is D μkg2+v40r2
Force acting at the center of hoop are :
  • Normal force N upwards
  • mg downwards.

Centripetal acceleration, ac=v20r
Frictional force, F=μkN
N=m2g2+m2v40r2

Tangential acceleration, at=Fm

at=μkg2+v40r2

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