Question

Assertion: n small balls each of mass m colliding elastically each second on surface with velocity u. The force experienced by the surface is 2 mnu.
Reason: On elastic collision, the ball rebounds with the same velocity

• A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true statement but Reason is false
• D. If both Assertion and Reason are false statements.

Answer 1

Answer: (A)

If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

In elastic collision, there is no loss in energy. Thus, after the collision with the surface, the KE will be equal to that before collision. Hence, the speeds will not change, only direction changes. Change in momentum (per ball) = m(u-(-u)) = 2mu.

In t (1 sec) time n balls hit. Thus net avg. force on surface = $\Delta P/\Delta t$ = 2mu/(1/n) = 2mnu.