but \(\omega=\frac{v}{R}\)

\(\therefore\) Rotational \(K E=\frac{1}{2} I \frac{v^{2}}{R^{2}}\)

but the moment of inertia of a sphere is \(I=\frac{2}{5} m R^{2}\)

\(\therefore\) Rotational \(K E=\frac{1}{2}\left(\frac{2}{5} m R^{2}\right) \frac{v^{2}}{R^{2}}\)

\(\mathrm{Or}\)

Rotational \(K E_{R}=\frac{1}{5} m v^{2}\)

Translational \(K E_{T}=\frac{1}{2} m v^{2}\)

Ratio \(\frac{K E_{R}}{K E_{T}}=\frac{\frac{1}{5} m v^{2}}{\frac{1}{2} m v^{2}}=\frac{2}{5}\)