A light string passing over a smooth light pulley connects two blocks of masses m 1 and m 2 (where m 2 m 1 ). If the acceleration of the system is frac g √(2) , then the ratio of the masses frac m 1 m 2 is :

Physics · Newton's Laws of Motion

JEE Main 2024 — 6 April, Shift 1 — Question 45

A light string passing over a smooth light pulley connects two blocks of masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$ (where $\mathrm{m}_{2}>\mathrm{m}_{1}$ ). If the acceleration of the system is $\frac{\mathrm{g}}{\sqrt{2}}$ , then the ratio of the masses $\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}$ is :

Option A:
$\frac{\sqrt{2}-1}{\sqrt{2}+1}$
Correct
Option B:
$\frac{1+\sqrt{5}}{\sqrt{5}-1}$
Option C:
$\frac{1+\sqrt{5}}{\sqrt{2}-1}$
Option D:
$\frac{\sqrt{3}+1}{\sqrt{2}-1}$

Answer: A

Step-by-step solution

$a=\left(\frac{M_{2}-M_{1}}{M_{1}+M_{2}}\right) g$

$\frac{g}{\sqrt{2}}=\left(\frac{M_{2}-M_{1}}{M_{1}+M_{2}}\right) g$ $\left(M_{1}+M_{2}\right)=\sqrt{2} M_{2}-\sqrt{2} M_{1}$ $\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}=\left(\frac{\sqrt{2}-1}{\sqrt{2}+1}\right)$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 6 April, Shift 1
Subject: Physics
Chapter: Newton's Laws of Motion
Topic: Pulley - Block Problems