Question

Two identical balls in which one is moving with a velocity given as $12m{{s}^{-1}}$ and the second one is at rest, are colliding elastically. After collision velocity of the second ball and the first ball can be given as,
$\begin{aligned} & A.6m{{s}^{-1}},6m{{s}^{-1}} \\\ & B.12m{{s}^{-1}},12m{{s}^{-1}} \\\ & C.12m{{s}^{-1}},0m{{s}^{-1}} \\\ & D.0m{{s}^{-1}},12m{{s}^{-1}} \\\ \end{aligned}$

Answer 1

Elastic collision is a kind of collision in which the energy as well as momentum of a body has been conserved. As we all know the coefficient of restitution of the elastic collision will be equal to one. Which using this finds the velocities of both the balls after the collision. This will help you in answering this question.

Complete answer:
Elastic collision is a kind of collision in which the energy as well as momentum of a body has been conserved.
Therefore as we all know, the coefficient of restitution for a perfectly elastic collision will be equivalent to one. This can be written as,
$e=1$
The coefficient of restitution becoming one means that there will be exchange in the velocity of the bodies. That is the velocity of one of the bodies undergoing collision will be exchanged with the velocity of the other one which is taking part in the collision.
As the velocity of the second ball before collision has been mentioned as,
${{u}_{2}}=0$
Therefore the velocity of first ball after collision will become,
${{v}_{1}}=0$
In the same sense, the velocity of the first ball before the collision has been mentioned as,
${{u}_{1}}=12m{{s}^{-1}}$
Therefore the velocity of the second ball after the collision will be obtained as,
${{v}_{2}}=12m{{s}^{-1}}$

Hence, the correct option is option D.

Note:
The Coefficient of Restitution is defined as the measure of the bounciness of a collision between two bodies. Or it is the measure of how much of the kinetic energy will stay for the bodies to rebound from one another to the measure how much is lost as heat or work.