Two blocks `M_(1)` and `M_(2)` having equal mass are free to move on a horizontal frictionless surface. `M_(2)` is attached to a massless spring as shown in figure. Initially `M_(2)` is at rest and `M_(1)` is moving toward `M_(2)` with speed `upsilon` and collides head-on with `M_(2)`.

Options

A. While spring is fully compressed all the `KE` of `M_(1)` is stored as `PE` of spring.
B. While spring is fully compressed the system momentum us not conserved, though final momentum is equal to initial momentum
C. If spring is massless, the final state of the `M_(1)` is state of rest.
D. If the surface on which blocks are moving has friction, then collision cannot be elastic.
.

Answer

C

Explanation

Consider the adjacent diagram when `M_(1)` comes in contact with the spring, `M_(1)` is retarded by the spring force and `M_(2)` is accelerated by the spring force.
(a) The spring will continue to compress until the two blocks acquire common velocity.
(b) As surfaces are frictionles momentum of the system will be conserved.
( c) If spring is massless whole enegry of `M_(1)` will be imparted to `M_(2)` and `M_(1)` will be at rest, then
(d) Collision is inelastic, even if friction is not involved.
.