Answer
$a=6.53m/s^{2}$
Work Step by Step
If a is the acceleration of center of mass,
Mg-2T=Ma ........ equation (1)
Net torque about axis of cylinder,
2T.R=I $\times$ angular acceleration
$2T.R=I\times\frac{a}{R}$
$2T=\frac{I}{R^{2}}.a$, where $I=\frac{1}{2}MR^{2}$
So, $2T=\frac{Ma}{2}$ .......... equation (2)
From equations (1) & (2), we have
$a=6.53m/s^{2}$
