Two bodies of masses 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity g is

Given,  $m_1=4 \mathrm{kg},m_2=6 \mathrm{kg}\text{ and }a=?$

The free body diagram of given system is shown below

The balancing equations for given system are

          $T-m_{1}g=m_{1}a$                                     …(i)

and   $m_{2}g-T=m_{2}a$                                      … (ii)

Adding Eqs. (i) and (ii), we get

$m_{2}g-m_{1}g=m_{1}a+m_{2}a$

$\Rightarrow a=\left(\frac{m_2-m_1}{m_1+m_2}\right)·g=\left(\frac{6-4}{4+6}\right)\times g=\frac{g}{5}$