d
Let the acceleration of the mass be \(a\).

Let the angular acceleration of the disc be \(\alpha .\)

since the string moves without slipping on the disc,

\(a=R \alpha\)

\(a=\frac{m g-T}{m}\)

\(T=m g-m a.....(1)\)

\(\alpha=\frac{\tau}{I}\)

where \(\tau=\) torque \(=T R\)

and \(I=\frac{M R^{2}}{2}\)

\(T=\frac{M a}{2}\)

From \((1)\) and \((2)\)

\(a=\frac{2 m g}{m+2 M}\)

\({V}^{2}={u}^{2}+2as\)

\(u=0\)

\(s=h\)

\(V=\sqrt {\dfrac {4mgh}{2m+M}}\)