Question

Two blocks A and B of masses m and 2m respectively pass over a pulley and are held at rest such that the spring is in natural length. Find out the accelaration of the blocks just after the release. Options are- ( for A and B respectively in order)-

Answer 1

Option (b)

Let us assume that the block A of mass m is tied to the spring. However at t=0s, the spring is not compressed or extended.

Let T be the tension in the string going over pulley.   Just after releasing the force on block A, both blocks move with the same acceleration. The tension is same in the rope on both sides.  The equations of motion for both blocks are: 
         T - m g = m a
         2mg - T = 2m a

So   mg = 3 m a   =>  a = g/3

So at t = 0, block A moves up initially with an acceleration g/3 and block B moves down with acceleration g/3.

Answer 2

This may help you for understanding