The block of mass M moving on a frictionless horizontal surface collides with a spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is

When block of mass M collides with the spring, its kinetic energy gets converted into elastic potential energy of the spring. From the law of conservation of energy, conservation of energy KE = energy stored in a spring 12Mv2=12kL2⇒∴v=kMLhere M is mass, length of compression in spring =LWhere v is the velocity of block by which it collides with spring. So its maximum momentum, momentum=p=Mv=MkML=MkLAfter collision, the block will rebound with same linear momentum.