MHT CET · Physics · Laws of Motion

\(10^{23}\) molecules of a gas, each having a mass of \(3 \times 10^{-27} \mathrm{~kg}\) strike per second per sq.cm of a rigid wall at an angle of \(60^{\circ}\) with the normal and rebound with a velocity of \(500 \mathrm{~m} / \mathrm{s}\). The pressure exerted by the gas molecules on the wall is

A \(2000 \mathrm{~N} / \mathrm{m}^2\)
B \(500 \mathrm{~N} / \mathrm{m}^2\)
C \(1000 \mathrm{~N} / \mathrm{m}^2\)
D \(1500 \mathrm{~N} / \mathrm{m}^2\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(1500 \mathrm{~N} / \mathrm{m}^2\)

Step-by-step Solution

Detailed explanation

According to the Newton's second law of motion:
\(\text {Pressure exerted on the wall}\) \(=\frac{\text { Rate of change of mometum } \times \text { no. of molecules }}{\text { Area }}\)
\(\Rightarrow P=\frac{\left(2 m V \cos 60^{\circ}\right) \times N}{A}=\) \(\frac{2 \times 3 \times 10^{-27} \times 5 \times 10^{-2} \times \cos 60^{\circ} \times 10^{23}}{10^{-4}}\)
\(\therefore P=1500 \mathrm{~N} / \mathrm{m}^2\)

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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