Physics · Newton's Laws of Motion

JEE Main 2025 — 28 January, Evening Shift — Question 63

A balloon and its content having mass $M$ is moving up with an acceleration ' $a$ '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' $3 \mathrm{a}^{\prime}$ will be : (Take ' g ' as acceleration due to gravity)

Option A:
$\frac{3 \mathrm{Ma}}{2 \mathrm{a}-\mathrm{g}}$
Option B:
$\frac{3 \mathrm{Ma}}{2 \mathrm{a}+\mathrm{g}}$
Option C:
$\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}$
Correct
Option D:
$\frac{2 \mathrm{Ma}}{3 \mathrm{a}-\mathrm{g}}$

Answer: C

Step-by-step solution

$\mathrm{F}-\mathrm{mg}=\mathrm{ma}$

$F=m a+m g$

$F-(m-x) g=(m-x) 3 a$

Put F

$\mathrm{Ma}+\mathrm{mg}-\mathrm{mg}+\mathrm{xg}=3 \mathrm{ma}-3 \mathrm{xa}$

$x=\frac{2 m a}{g+3 a}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Evening Shift
Subject: Physics
Chapter: Newton's Laws of Motion
Topic: Free Body Diagrams and Constraint Relations