A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system

Initial momentum = mvFinal momentum = (m+M)VBy conservation of momentum  mv=(m+M)V∴ Velocity of (bag + bullet) system V=mvM+m∴ Kinetic energy =  12(m+M) V2=12(m+M)mvM+m2=12m2v2M+m