If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km / s , the root mean square velocity of oxygen at the same condition in km / s is :

Physics · Kinetic Theory of Gases

JEE Main 2024 — 1 February, Shift 2 — Question 43

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2 \mathrm{~km} / \mathrm{s}$ , the root mean square velocity of oxygen at the same condition in $\mathrm{km} / \mathrm{s}$ is :

Option A:
2
Option B:
0.5
Correct
Option C:
1.5
Option D:
1

Answer: B

Step-by-step solution

$\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$

$\frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}}=\sqrt{\frac{\mathrm{M}_{2}}{\mathrm{M}_{1}}} \Rightarrow \frac{2}{\mathrm{~V}_{2}}=\sqrt{\frac{32}{2}}$

$\mathrm{V}_{2}=0.5 \mathrm{~km} / \mathrm{s}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 2
Subject: Physics
Chapter: Kinetic Theory of Gases
Topic: Pressure of Gas and Different speeds of Gas Molecules