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

(b) Rotational energy `= (1)/(2) I (omega)^2 = (1)/(2) (mK^2) omega^2`
Linear kinetic energy `= (1)/(2) m omega^2 R^2`
=`((1)/(2) (mK^2) omega^2)/((1)/(2) (mK^2) omega^2 + (1)/(2) m omega^2 R^2) = (K^2)/(K^2 + R^2)`.