Explanation

(c) The kinetic energy of the solid sphere,
$K = \frac{1}{2}Mv^{2}$ …(i)
The rotational kinetic energy,
$K_{r} = \frac{1}{2}\ I\omega^{2}$
But $I = \frac{2}{5}MR^{2}$ for solid sphere and $\omega = \frac{v}{R}$
then, $K_{r} = \frac{1}{2} \times \frac{2}{5}MR^{2} \times \frac{v^{2}}{R^{2}}$
$K_{r} = \frac{1}{5}Mv^{2}$ …(ii)
On dividing Eq. (ii) by Eq. (i), we have
$\frac{K_{r}}{K} = \frac{\frac{1}{5\ Mv^{2}}}{\frac{1}{2\ Mv^{2}}}$
or $\frac{K_{r}}{K} = \frac{2}{5}$