a
From the codition of equilibrium 

\(mg - T = ma \)            \(....(i)\)

\(RT =\)  \(I\alpha \)

\(\begin{array}{l}
\overline a  = \overline \alpha   \times R\,and\,I = \frac{{M{R^2}}}{2}\\
\,\,\,\,\,\,\,\,\,\,\,RT = \frac{{M{R^2}}}{2}.\frac{a}{R}
\end{array}\)

Tension in string,

\(T = \frac{{Ma}}{2}\)                 From equation \((i)\)

\(mg - \frac{{Ma}}{2} = ma\)

\( \Rightarrow mg = a\left( {\frac{M}{2} + m} \right) \Rightarrow mg = a\left( {\frac{{M + 2m}}{2}} \right)\)

Hence, acceleration of the body,

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