Ncert Exercises & Solutions

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 $v$ and collides head-on with $M_2.$

Consider the following given statements:

(a).	while spring is fully compressed, all the kinetic energy of $M_1$ is stored as potential energy of spring.
(b).	while spring is fully compressed, the system's momentum is 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.

Choose the correct option:

1.	only (a)
2.	(a), (b)
3.	(b), (c)
4.	(c), (d)

Hint: Apply the concept of conservation of momentum.

Step 1: Analyse each option to find the correct answer.

Consider the adjacent diagram when $M_{1}$ $M_{1}$ comes in contact with the spring, M, is retarded by the spring force, and $M_{2}$ $M_{2}$ is accelerated by the spring force.

(a) The spring wilt continue to compress until the two blæks acquire cornrnon velocity.

(b) As surfaces are frictionless momentum of the system will conserved.

(c) If spring is massless whole energy of $M_{1}$ $M_{1}$ will be imparted to $M_{2}$ $M_{2}$ and $M_{1}$ $M_{1}$ will be at rest, then

(d) Collision is inelastic, even if friction is not involved.

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