A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is `k`. If radius of the ball be `R`, then the fraction of total energy associated with its rotation will be.

Options

A. `(k^(2))/(R^(2))`
B. `(k^(2))/(k^(2)+R^(2))`
C. `(R^(2))/(k^(2)+R^(2))`
D. `(k^(2)+R^(2))/(R^(2))`

Explanation

`(K_(g))/(K)=((1)/(2)mv^(2)xx(k^(2))/(R^(2)))/((1)/(2)mv^(2)(1+(k^(2))/(R^(2))))=(k^(2))/(k^(2)+R^(2))`