Two 30 kg blocks rest on a massless belt which passes over a fixed pulley and is attached to a 40 kg block. If coefficient of friction between the belt and the table as well as between the belt and the blocks B and C is and the system is released from rest from the position shown, the speed with which the block B falls off the belt is/are: (Take g =10 ~m / s ^2 )

Step-by-step solution

Maximum possible acceleration of block will be = g . (i) When =0.2 maximum acceleration possible so that block does not slip is 2 ~m / s ^2 Now acceleration of system assuming blocks don't slip is a = 40 ~g -2 mg 100 =2.8 ~m / s ^2 =0.2 as 2.8 2 . Hence the assumption is wrong and then blocks slip on the belt. Maximum force applicable on block B is mg acc. of block =2 ~m / s ^2 Hence velocity of B when it strikes pulley is V ^2=0^2+(2 2 2)V^2=8 V=2 2 ~m / s Hence (A). (ii) When =0.5 maximum acceleration possible so