Question

A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on heating the war with the same velocity rebounds back. It can be concluded that
A. Metal ball suffers a greater change in momentum
B. Rubber balls suffer a greater change in momentum
C. The initial momentum of the metal ball is greater than the initial momentum of the rubber ball.
D. Both suffer the same change in momentum

Answer 1

Hint: Elasticity is the property of the body to return back to its original shape after getting deformed. Rubber ball has high elasticity, therefore when it hits the wall it gets compressed and due to elasticity, it quickly returns to its original shape. While doing this it pushes back on the wall. Thus, it rebounds back. When a metal ball hits the wall most of its energy is transferred to the wall and the ball can be said to have zero velocity. The final velocity of the rubber ball will be equal and opposite to the initial velocity
The change in momentum can be calculated as
$\Delta P = m({v_2} - {v_1})$
Where m is the mass, ${v_2}$ is the final velocity, and ${v_1}$ is the initial velocity.
By finding the change in momentum for both the ball and comparing the values obtained we can arrive at the correct answer.

Complete step by step answer:
A metal ball hits a wall and does not rebound whereas a rubber ball with the same mass and velocity will rebound. This is due to the elasticity of the rubber ball. Elasticity is the property of the body to return back to its original shape after getting deformed. Rubber ball has high elasticity, therefore when it hits the wall it gets compressed and due to elasticity, it quickly returns to its original shape. While doing this it pushes back on the wall. Thus, it rebounds back.
Let the mass of both the metal ball and rubber ball be $m$.
Let the velocity of both balls be $v$ initially.
In the case of a metal ball, the kinetic energy with which it is thrown will be transferred to the wall. Since the shape of the metal body cannot be deformed easily, almost all energy will be used on the wall. Hence the ball will lose energy and fall down.
So, we can take the final velocity of the metal ball to be zero.
The change in momentum can be calculated as
$\Delta P = m({v_2} - {v_1})$
Where m is the mass, ${v_2}$ is the final velocity, and ${v_1}$ is the initial velocity.
Substituting the values for the metal ball, we get a change in momentum of the metal ball as
$\Delta {P_m} = m(0 - v) = - mv$
$\because {v_2} = 0$
In the case of a rubber ball, it rebounds back with almost the same velocity. So we can take the final velocity and initial velocity at the same value, $v$. The direction in which it is rebounded is opposite to that of the initial direction. So we need to take a negative sign.
Now the change in momentum of the rubber ball can be given as
$\Delta {P_r} = m( - v - v) = - 2mv$
We can see that the change in momentum of the rubber ball is greater than the change in momentum of the metal ball.

Therefore, the correct answer is option B. Rubber ball suffers a greater change in momentum.

Note:
While substituting for the final velocity in the case of rubber ball remember to consider the direction. The direction of the initial velocity in which the ball is thrown is taken in a positive direction. When it rebounds the direction will be reversed. So, remember to put a negative sign in the case of velocity when it rebounds.