Answer
$$
\begin{aligned}
v^{2} &=\frac{2 m g h}{m+I / r^{2}} \\
&=\frac{2 g h}{1+I^{*}}
\end{aligned}
$$
where, $I^{*}=I / r^{2}$
Work Step by Step
$$
\begin{aligned}
m g h &=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2} \\
&=\frac{1}{2}\left(m+I / r^{2}\right) v^{2},
\end{aligned}
$$
Thus, we have:
$$
\begin{aligned}
v^{2} &=\frac{2 m g h}{m+I / r^{2}} \\
&=\frac{2 g h}{1+I^{*}}
\end{aligned}
$$
where, $I^{*}=I / r^{2}$
