Question

Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\,m{s^{ - 1}}$. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is
A. $0.4\,m{s^{ - 1}}$
B. $0.2\,m{s^{ - 1}}$
C. $0.1\,m{s^{ - 1}}$
D. $0.05\,m{s^{ - 1}}$

Answer 1

Hint: In order to solve this question, we will use the concept of head on elastic collision in which when two bodies of same mass collide with each other the body which was at rest gets whole energy of moving body, so using this we will determine the velocity of the fourth and last ball.

Complete step by step solution:
Elastic collisions are those where total momentum of the system before the collision is always equal to the final momentum of the system after the collision and total kinetic energy of the system before the collision is equal to the final kinetic energy of the system after the collision and in between these bodies interchange the velocities with different magnitudes.

But in head on elastic collision between two bodies of equal mass and if one of the bodies was at rest before the collision then after the collision the moving body comes to rest and the body which was at rest initially starts moving with the same velocity with which another body was moving.

Here, we have given four balls of equal mass and all was at rest initially and first body starts moving with velocity of $0.4\,m{s^{ - 1}}$ and when it hits second body as head-on collision second body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from first body and later third body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from second body and at last fourth body will acquired the velocity of $0.4\,m{s^{ - 1}}$ from third body. So the final velocity of the last and fourth ball is $0.4\,m{s^{ - 1}}$.

Hence, the correct answer is option A.

Note: It should be remembered that, when the last ball will acquire the velocity it will simply continue to move with same velocity if there are no resistive forces and if bodies were of different mass then all bodies acquire different velocities depending upon the mass.