A bag of sand of mass M is suspended by a string. A bullet of mass m is fired at it with velocity v and gets embedded into it. The loss of kinetic energy in this process is

Initial kinetic energy of bullet = 12mv2After inelastic collision system moves with velocity V By the conservation of momentum mv+0=(m+M) V⇒V=mvm+MKinetic energy of system =  12(m+M) V2=  12(m+M) mvm+M2Loss of kinetic energy =  12mv2−12(m+M) mvm+M2= 12mv2Mm+M