Assertion: A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on hitting the wall with the same velocity rebounds back.

Reason: Rubber ball suffers a greater change in momentum than metal ball.

CONCEPT:

• Elasticity: The property of a body by virtue of which the body can recover its original shape and size after removal of the deforming force.

• Momentum (p): The product of mass and velocity is called as the momentum of the body.

Momentum (p) = m × V

Where, m = mass of the body, and V = velocity of the body.

CALCULATION:

Given that,

For rubber ball:

The initial momentum of the rubber ball as it was thrown towards the wall, p1 = p

Final momentum of the rubber ball as it bounces back from the wall, p2 = -p

Whereas the net change in momentum Δp can be given as

\({\rm{\Delta }}p = {p_1} - {p_2} = p - \left( { - p} \right) = 2p\)

For metal ball:

The initial momentum of the rubber ball as it was thrown towards the wall, p1 = p

Final momentum of the rubber ball as it bounces back from the wall, p2 = 0 (Since it comes in rest after striking the wall)

Whereas the net change in momentum Δp can be given as

\({\rm{\Delta }}p = {p_1} - {p_2} = p - \left( { 0} \right) = p\)

• Since the rubber is more elastic than the metal. that's why the rubber ball rebounds and the metal ball comes in rest. So the assertion is correct.
• As the change in momentum of the rubber ball is more than that in the case of metal ball. So the reason is also correct. But the reason is not the correct explanation for the assertion because the correct reason is elasticity. Hence option 2 is correct.