In the system shown in figure mB = 4kg, and mA = 2 kg. The pulleys are massless and friction is absent everyrwhere. The acceleration of block A  is

For movable pulleyaB = O+aA2aA = 2aB--------(i)Free body diagrams of A and B: Equation of motion of block A and BFor A : T-mAg2 = mAaA = mA(2aB)-----(ii)For B : mBg-2T = mBaB-------------(iii)From (ii) and (iii) [2(ii) + (iii)]mBg-mAg = [4mA+mB]aB⇒aB = [mB-mA]g[4mA+mB] = [4-2]×10[4×2+4]           = 2012 = 53m/s2Hence  aA = 2aB = 103m/s2