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 elastically , the maximum compression in the spring is

detailed solution

Correct option is A

After striking with A, the block C comes to rest and block A moves with velocity v. When compression in spring ismaximum, both A and B will be moving with common velocity v.From law of conservation of linear momentum,                             mv=(m+m)V⇒V=v2                        …(i)From law of conservation of energy,          KE of block C = KE of system + PE of system                12mv2=12(2m)v2+12kx2⇒            12mv2=12(2m)v22+12kx2                    [from Eq. (i)]⇒                kx2=12mv2⇒x=vm2k