Choose the correct option:
A small collar of mass `m` is given an initial 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 traveled before the collar comes to rest. (Recognize that the friction force depends on the net normal force).

Options

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

Answer

D