Two identical blocks A and B, each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is

Initial momentum of the system (block C) = mvAfter striking with A, the block C comes to rest and now both block A and B moves with velocity V, when compression in spring is maximum.By the law of conservation of linear momentum mv = (m + m) V ⇒V=v2By the law of conservation of energy K.E. of block C = K.E. of system + P.E. of system  12mv2=12(2m) V2+12kx2⇒12mv2=12(2m) v22+12kx2⇒kx2=12mv2⇒x=vm2k