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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 μk√g2+v40r2Force acting at the center of hoop are :Normal force N upwards mg downwards.Centripetal acceleration, ac=v20r Frictional force, F=μkNN=√m2g2+m2v40r2Tangential acceleration, at=Fm⟹at=μk√g2+v40r2

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