Question

A particle of mass \[m\] strikes another particle of the same mass at rest. Find the angle between the velocities of the particle after the collision, if the collision is elastic.
(A) \[\dfrac{\pi }{2}\]
(B) \[\dfrac{\pi }{3}\]
(C) \[\dfrac{\pi }{8}\]
(D) Zero

Answer 1

Hint: In the given question, an object of a given mass is colliding with another identical mass at rest. We have been told that the collision will be elastic; that means both the energy and the momentum of the particles before and after the collision will be conserved. So to obtain the required result, we will apply momentum conservation on the two particles.

Complete step by step solution:
Since in the given question, the masses are the same and the collision is elastic; when we apply conservation of momentum on the particles, the momentum of the first mass will be transferred to the second mass particle. Since the masses are identical, transferred momentum means that the second mass will acquire the velocity of the first particle.
The second particle will continue moving with the same velocity, along the same line of motion as the first particle. The first particle, having transferred the momentum to the second particle, will come to rest after the collision.
We can say that the angle between the velocities of the particles after the collision will be zero.

Therefore, option (D) is the correct answer to the given question.

Note:
In the given question, the particle suffers an elastic collision with another identical particle and hence comes to rest after collision. If the particle had collided with a wall or any rigid body, it would have retraced its path with the same velocity with which it collided with the wall. Whereas, if the particle suffers an inelastic collision, it sticks to the other particle and behaves as a combined mass system.