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 `)`

Options

A. `mu_(k)sqrt(g^(2)+(V_(0)^(4))/(r^(2))`
B. `mu_(k)g`
C. `mu_(k)((V_(0)^(2))/(r))`
D. None of these

Answer

C

Explanation

`K.E. =(1)/(2)1_(cm)omega^(2)+(1)/(2)mV_(cm)^(2)=(1)/(2)(Ml^(2))/(12)(V_(0)^(2))/(l^(2))+(1)/(2)M((3)/(2)V_(0))^(2)=(7)/(6)MV_(0)^(2)`