Answer
$1.2m/s^{2}$
Work Step by Step
$m_{2}g-T_{2}=m_{2}a$
or, $T_{2}=m_{2}(g-a)$ ........... equation (1)
$T_{1}-m_{1}g=m_{1}a$
or, $T_{1}=m_{1}(g+a)$ ........... equation (2)
Also, $T_{2}-T_{1}=\frac{T}{r}$ .......... equation (3)
From equations (1), (2), (3), we have
$a=\frac{(m_{2}-m_{1})g-\frac{T}{r}}{m_{1}+m_{2}}=1.2m/s^{2}$
