A body rolls without slipping. The radius of gyration of the body about an axis passing through its centre of mass is `K`. The radius of the body is `R`. The ratio of rotational kinetic energy to translational kinetic energy is.

Options

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

Answer

A

Explanation

(a) `(Rotational K.E.)/(Translational K.E.) = ((1)/(2) I omega^2)/(1/(2) mv)= (m K^2 (v^2)/(R^2))/(mv^2) = (K^2)/(R^2)`.