MHT CET · Physics · Center of Mass Momentum and Collision

A wall is hit elastically and normally by ' \(n\) ' balls per second. All the balls have the same mass ' \(m\) ' and are moving with the same velocity ' \(u\) '. The force exerted by the balls on the wall is

A \(2 \mathrm{mnu}^2\)
B \(2 \mathrm{mnu}\)
C \(\frac{1}{2} \mathrm{mnu}^2\)
D \(\mathrm{mnu}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \mathrm{mnu}\)

Step-by-step Solution

Detailed explanation

The correct option is (B).
Force is related to momentum change by following relation,
\(\mathrm{F}=\frac{\mathrm{dp}}{\mathrm{dt}}\)
Momentum change per second, \(\frac{\mathrm{dp}}{\mathrm{dt}}=\mathrm{n}(\mathrm{mu}-(-\mathrm{mu}))=2 \mathrm{nmu}\)
Therefore,
\(\mathrm{F}=2 \mathrm{nmu}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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