Each pulley in the figure has radius r and moment of inertia I. The acceleration of the block is

T1−mg=ma……..(i)rT2−T1=Iα.........(ii)Mg−T3=Ma.........(iii)rT3−T2=Iα.........(iv)and a = RαFrom Eqs. (ii) and (iv), we getT3−T1=2Iαr=2IaR2From Eqs. (i) and (iii), we get(M−m)g=(M+m)a+T3−T1⇒(M−m)g=(M+m)a+2Iar2⇒a=(M−m)gM+m+2Ir2