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))`

Answer

B

Explanation

`("Rotational KE")/("Total KE")((1)/(2)mv^(2)((K^(2))/(R^(2))))/((1)/(2)mv^(2)(1+(K^(2))/(R^(2))))=(K^(2))/(K^(2)+R^(2))`