$$ \begin{aligned} & \mathrm{I}_1=\frac{\mathrm{M}(2 \mathrm{~L})^2}{12}=\frac{\mathrm{ML}^2}{3} \\ & \mathrm{I}_2=\mathrm{I}_1+2 \frac{\mathrm{~mL}^2}{4}=\frac{\mathrm{ML}^2}{3}+\frac{\mathrm{mL}^2}{2} \\ & \omega \propto \frac{1}{\sqrt{ } \mathrm{I}} \end{aligned} $$ $$ \frac{\omega_1}{\omega_2}=\frac{1}{0.8}=\sqrt{\frac{\frac{M}{3}+\frac{m}{2}}{\frac{M}{3}}} \quad \Rightarrow \frac{m}{M}=0.375 $$