Question

A metal ball does not rebound when struck on a wall, whereas a rubber ball of same mass when thrown with the same velocity on the wall rebounds. From this it is inferred that:
A. change in momentum is same in both
B. change in momentum in rubber ball is more
C. change in momentum in metal ball is more
D. initial momentum of metal ball is more than that of rubber ball

Answer 1

Hint: We will use the formula of momentum. As two objects are given we will calculate the momentum for both the objects and compare them. Initial and final momentum for both the objects has been calculated.
Formula used:
Momentum \[P=mv\]

Complete answer:
When we throw a metal ball on a wall that does not rebound and when we throw a rubber ball of same mass as that of a metal ball and with the same velocity as that of a metal ball, it rebounds. We need to know the reason why it happened.
For this we can calculate the momentum of a rubber ball and metal ball.
Let us first calculate the momentum for the metal ball.
Assume the mass of metal ball be m and velocity be v
Thus initial linear momentum will be \[{{P}_{i}}=mv\]
According to the question the metal ball does not rebound so final velocity will be zero, so the final momentum will be zero.
Now we will calculate momentum for the rubber ball.
Given that the rubber ball rebound from the wall
Therefore initial velocity \[{{P}_{i}}=mv\]
Final velocity \[{{P}_{f}}=-mv\]
Negative sign indicates that the ball travels in the opposite direction to initial velocity.
Therefore change in momentum
\[\begin{align}
  & \Delta P={{P}_{i}}-{{P}_{f}} \\
 & =2mv
\end{align}\]
So we can conclude that the momentum of a rubber ball is more than that of a metal ball.

Therefore option B is correct.

Note:
Momentum refers to the motion of an object, depending upon its mass and velocity. Newton’s second law follows the principle of momentum. Regardless of having the same mass and velocity of both the objects the momentum varies according to its initial and final velocity.