using conservation of mechanical energy
$$
\begin{aligned}
& m g 2 R=\frac{1}{2} I_{u=\omega^2} \omega^2+\frac{1}{2} I_{\text {partac }} \omega^2 \\
& m g 2 R=\frac{\omega^2}{2}\left[\frac{m R^2}{2}+m R^2\right] \\
& m g 2 R=\frac{\omega^2}{2} \frac{3}{2} m R^2 \\
& \frac{3}{4} \omega^2=\frac{2 g}{R} \\
& \omega^2=\frac{8 g}{3 R} \\
& \omega=\sqrt{\frac{80}{3 R}}
\end{aligned}
$$
Given
$$
\begin{aligned}
& \omega=4 \sqrt{\frac{x}{3 R}} \\
& 16 \frac{x}{3 R}=\frac{80}{3 R} \\
& x=5
\end{aligned}
$$