Two blocks of masses 8 kg and 12 kg are connected at the two ends of a light inextensible string. The string passes over a frictionless pulley. The acceleration of the system is

Let a be the common acceleration of the system and T be tension of the string.

The equations of motion of two blocks are

$$\begin{gathered} T-8g=8a \dots \left(i\right) \\ and 12g-T=12 a \dots \left(ii\right) \\ On adding \left(i\right) and \left(ii\right), we get \\ 4g=20a or a=\frac{g}{5} \end{gathered}$$