Two blocks M and M having equal mass are free to move on a horizontal frictionless surface. M is attached to a massless spring as shown in figure. Initially M is at rest and A/, is moving toward M with speed v and collides head-on with M . (a) While spring is fully compressed all the K•E of Myis stored as PE of spring. (b) While spring is fully compressed the system momentum is not conserved, though final momentum is equal to initial momentum. (c) If spring is massless, the final state of the M is state of rest. (d) If the surface on which blocks are moving has friction, then collision cannot be elastic.

Ans: (c, d) If this is not specified we always consider the collision elastic.

When two bodies of equal mass collides elastically. Then, their velocities are interchanged in these types of collision. 

In elastic collision Kinetic energy and linear momentum(p) remains conserved.  

When masses M comes in contact with the spring. Then, M is retarded by the spring force and m is accelerated by the spring force. 

(a) The spring will remain continue to compress until the two blocks acquires common velocity. So, some of the kinetic energy of block M store into P.E and some part of it stores into K.E of block M . So option (a) is incorrect. 

(b) As surfaces are frictionless(no friction), momentum of the system will be conserved. So, option (b) is also incorrect. 

(c) The two bodies of equal mass M, exchange their velocities in a head on elastic collision between them. So, if the spring is massless, the final state of the mass M is state of rest. 

(d) Since, there is a loss of Kinetic energy, when the blocks collides on the rough surface. Hence, the collision is inelastic collision.