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COM in Collision and Explosion

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Question

Two blocks $M_{1}$ and $M_{2}$ having equal masses are 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 $v$ and collides head-on with $M_{2}$

While spring is fully compressed, all the kinetic energy of

M_{1}

is stored as potential energy of spring

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While spring is fully compressed, the system's momentum is not conserved, though final momentum is equal to initial momentum

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If spring is massless, the final state of the

M_{2}

is state of rest

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If the surface on which blocks are moving has friction, then collision cannot be elastic

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Solution

The correct option is D If the surface on which blocks are moving has friction, then collision cannot be elastic
If it is not specified we always consider the collision elastic.
When two bodies of equal masses collide elastically, their velocities are interchanged in these types of collisions.

Kinetic energy and linear momentum remain conserved.

According to the above 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.

The spring will continue to compress until the two blocks acquire common velocity. So some of kinetic energy of block $M_{x}$ store into P.E and some part of it stores into K.E of block $M_{1} a n d M_{2}$ . So option $(A)$ is incorrect.
As surfaces are frictionless momentum of the system will be conserved. So option $(B)$ is also incorrect.
The two bodies of equal mass exchange their velocities in a head-on elastic collision between them. So, if spring is massless, the final state of the $M_{1}$ is a state of rest, not $M_{2}$ . option $(C)$ is also incorrect
(d) Since there is a loss of K.E when the blocks collide on the rough surface. Hence, the collision is inelastic.
So correct option is $(D)$ .

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Two blocks M1 and M2 having equal masses are to move on a horizontal frictionless surface. M2 is attached to a massless spring as shown in figure. Initially, M2 is at rest and M1 is moving toward M2 with speed v and collides head-on with M2

Two blocks $M_{1}$ and $M_{2}$ having equal masses are 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 $v$ and collides head-on with $M_{2}$