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

T1−mg=ma  .....(i)rT1−T2=Iα   ......(ii)Mg−T3=Ma   ......(iii)rT2−T3=Iα   ......(iv)and a = RFrom Eqs. (ii) + (iv), we getT1−T3=2IaR2From Eqs. (i) and (iii), we get⇒a=(M−m)gM+m+2Ir2