The acceleration of block B in the figure will be

When block m2 moves downward with acceleration a, the acceleration of mass rn I will be 2a because it covers double distance in the same time in comparison to m2.Let T be the tension in the string. By drawing the free body diagram of A and B, T=m12a                                    .......(i)m2g−2T=m2a                          ......(ii)By solving (i) and (ii),a=m2g4m1+m2