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 is not conserved, though final momentum is equal to intital momentum.
C. If spring is massless, the final state of `M_(1)` is state of rest.
D. If the surface on which blocks are moving has friction, then collision cannot be elastic.

Answer

C, D

Explanation

While spring is fully compressed, the entire K.E. of `M_(1)` is not stores as `P.E.` of spring as `M_(2)` may move. If spring is massless, then as `M_(1)=M_(2)`, velocities of `M_(1)` and `M_(2)` are interchanged on collision. `M_(1)` comes to rest, instead of `M_(2)`. Choise (c) is correct.
If surface on which blocks are moving has friction, loss of energy is involved. Collision cannot be eleastic. Choice (d) is correct.