Physics - Rotation Question with Solution | TestHub

Rotational energy of sphere $E_R=\frac{1}{2}I{\omega }^2$ For sphere, moment of inertia $\begin{array}{rl}I& =\frac{2}{5}m{R}^2\\ \therefore E_R& =\frac{1}{2}\left(\frac{2}{5}m{R}^2\right){\left(\frac{v}{R}\right)}^2\\ & =\frac{1}{5}m{v}^2\end{array}$ Translational kinetic energy $E_r=\frac{1}{2}m{v}^2$ $\begin{array}{rl}\therefore \text{ Total energy }& =\frac{1}{5}m{v}^2+\frac{1}{2}m{v}^2\\ & =\frac{7}{10}m{v}^2\end{array}$ $\therefore$ Required fraction $=\frac{\frac{1}{5}m{v}^2}{\frac{7}{10}m{v}^2}$ $=\frac{2}{7}$