A small collar of mass `m` is given an intial velocity of magnitude `v_(0)` on the horizontal circular track fabricated from a slender rod. If the coefficient of kinetic friction is `mu_(K)`, determine the distance travelled before the collar comes to rest. (Recognize that the friction force depends on the net normal force).

Options

A. `(r)/(mu)ln[(v_(0)^(2)+sqrt(v_(0)^(4)+r^(2)g^(2)))/(rg)]`
B. `(r)/(4mu)ln[(v_(0)^(2)+sqrt(v_(0)^(4)+r^(2)g^(2)))/(rg)]`
C. `(2r)/(mu)ln[(v_(0)^(2)+sqrt(v_(0)^(4)+r^(2)g^(2)))/(rg)]`
D. `(r)/(2mu)ln[(v_(0)^(2)+sqrt(v_(0)^(4)+r^(2)g^(2)))/(rg)]`

Answer

D