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A small hoop of mass m is given an initi...

A small hoop of mass `m` is given an initial velocity of magnitude `v_(0)` on the horizontal circular ring of radius `'r'`. If the coefficient of kinetic friction is `mu_(k)` the tangential acceleration of the hoop immediately after is release is `(` assume the horizontal ring to be fixed and not in contact with any supporting surface `)`

A

`mu_(k)g`

B

`mu_(k)(v_(0)^(2))/(r)`

C

`mu_(k)sqrt(g^(2)+(v^(2))/(r))`

D

`mu_(k)sqrt(g^(2)+(v_(0))/(r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
The free body diagram of hoop is
`:. `The normal reaction `N=sqrt(m^(2)g^(2)+(m^(2)v_(0)^(4))/r^(2))`
`:. ` Frictional force `=mu_(k)N=mu_(k)sqrt(m^(2)g^(2)+(m^(2)v_(0)^(4))/(r^(2)))`

`:. ` tangentail acceleration `=(mu_(k)N)/(m)`
`=mu_(k)sqrt(g^(2)+(v_(0)^(4))/(r^(2)))`
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