In the system shown in figure $m_1>m_2$ . System is held at rest by thread BC. Just after the thread BC is burnt.

acceleration of  $m_1$ will be equal to zero

acceleration of $m_2$  will be downwards

magnitude of acceleration of two blocks will be non-zero and unequal 

 magnitude of acceleration of both the blocks will be  $\left(\frac{m_1-m_2}{m_1+m_2}\right)g$