Physics - Rotation Question with Solution | TestHub

By conservation of angular momentum, $L_1=L_2$.

The rotational kinetic energy is given by $K=\frac{L^2}{2I}$.

The ratio of final to initial kinetic energy is $\frac{K_2}{K_1}=\frac{I_1}{I_2}$.

The moment of inertia of a solid sphere is $I=\frac{2}{5}M{R}^2$.

Given $R_2=\frac{R_1}{3}$, we have $I_2=\frac{2}{5}M{\left(\frac{R_1}{3}\right)}^2=\frac{I_1}{9}$.

Therefore, $\frac{K_2}{K_1}=\frac{I_1}{\frac{I_1}{9}}=9$.

Answer: $9$