Physics · Kinetic Theory of Gases

JEE Main 2024 — 6 April, Shift 1 — Question 44

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

Option A:
$\frac{1}{32}$
Option B:
$\frac{2 \sqrt{2}}{1}$
Correct
Option C:
$\frac{1}{4}$
Option D:
$\frac{1}{2 \sqrt{2}}$

Answer: B

Step-by-step solution

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

$\begin{array}{*{35}{r}}\Rightarrow \frac{{{\text{V}}_{{{\text{O}}_{2}}}}}{\text{ }\!\!~\!\!\text{ }{{\text{V}}_{\text{He}}}}& ~=\sqrt{\frac{{{\text{M}}_{\text{w},\text{He}}}}{{{\text{M}}_{\text{w},{{\text{O}}_{2}}}}}}\\{} & ~=\sqrt{\frac{4}{32}}=\frac{1}{2\sqrt{2}}\\\frac{\text{ }\!\!~\!\!\text{ }{{\text{V}}_{\text{He}}}}{\text{ }\!\!~\!\!\text{ }{{\text{V}}_{{{\text{O}}_{2}}}}} & ~=\frac{2\sqrt{2}}{1}\\\end{array}$

Answer key and solution verified before publishing.

Practise Kinetic Theory of Gases

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Physics
Chapter: Kinetic Theory of Gases
Topic: Pressure of Gas and Different speeds of Gas Molecules