Question

A body is rolling without slipping on a horizontal plane. The radius of body is $R$. If the ratio of rotational to translational kinetic energy is $\frac{9}{25}$, then the radius of gyration of the body is

• A. $\frac{5R}{3}$
• B. $\frac{9R}{25}$
• C. $\frac{3R}{5}$
• D. $\frac{25R}{9}$

Answer 1

The correct option is C $\frac{3R}{5}$

Rotational kinetic energy $K_R=\frac{1}{2}I{\omega }^2=\frac{1}{2}m{k}^2\times \frac{v^2}{R^2}(sinceI=m{k}^{2}andv=Rw)$

Translational kinetic energy $K_T=\frac{1}{2}m{v}^2$
$\frac{K_R}{K_T}=\frac{K^2}{R^2}=\frac{9}{25}$
$\Rightarrow K=\frac{3R}{5}$.