Two blocks of equal mass are tied with a light string which passes over a massless pulley as shown in figure. The magnitude of acceleration of centre of mass of both the blocks is (neglect friction every where):

mg sin 600-T = ma, T-mg sin 300 = maSolving them, we get a = g(3-1)4a1→  = -acos600i^-asin600j^ = -a2i^-a32j^a2→  = -a cos 300i^ + a cos 300j^ = -a32i^+a2j^Nowacm→ = m1a1→+m2a2→m1+m2 = -ma2(1+3)i^+ma2(1-3)j^2m          = a4[(1+3)i^+(1-3)j^]|acm→| = a4[(1+3)2+(1-3)2] = a2 =g(3-1)42