Two blocks of masses m and M are held against a compressed spring on a frictionless horizontal floor with the help of a light thread. When the thread is cut, the smaller block leaves the spring with a velocity u relative to the larger block. Find the recoil velocity of the larger block.

Explanation

When the thread is cut, the spring pushes both the block, and impart them momentum. The forces applied by the spring on both the block are internal forces of the two-block system. External forces acting on the system are weights and normal reactions on the blocks from the floor. These external forces have zeronet resultantof the system. In addition to this fact no external force acts on the system in horizontal direction, therefore, horizontal component of the total momentum of the system rmains conserved. Velocities of both the total momentum of the system remains conserved.
Velocities of both the objects relative to the ground (inertial frame) are shown in the adjoining figure.

Since before the thread is cut system was at rest, its total momentum was zero. Principle of conservation of momentum for the horizontal direction yields.
`underset(i = 1)overset(n)sum 1^(n)p_("horizontal")=0 rarr " " -Mv+m(u-v)=0`
`v=("mu")/(M+m)`