NEET 2016 Phase 1 · PhysicsRMS speedPrevious Year Question
The molecules of a given mass of a gas have r.m.s. velocity of 200 ms⁻¹ at 27 °C and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively 127 °C and 0.05 × 10⁵ Nm⁻², the r.m.s. velocity of its molecules in ms⁻¹ is:
Answer: (B) 400/√3. Correct Answer (B): 400/√3 ms⁻¹ The r.m.s.
- A.100√2
- B.400/√3✓
- C.100√2 / 3
- D.100 / 3
Correct Answer
(B) 400/√3
Solution & Explanation
Correct Answer (B): 400/√3 ms⁻¹ The r.m.s. speed of gas molecules is v_rms = √(3RT/M), so for a given gas it depends only on the absolute temperature — NOT on pressure. The pressure values quoted here are distractors. Since v_rms ∝ √T, raising the temperature from 300 K to 400 K increases the speed by the factor √(400/300) = 2/√3, giving 400/√3 ms⁻¹.
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