JEE Main 202528 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 28 January
Shift: Evening Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2025 · 28 January · Evening Shift · Physics · Center of Mass, Momentum and Collision

A balloon and its content having mass M is moving up with an...

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 a^{\prime}

will be (Take ' g ' as acceleration due to gravity) A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from

A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from

Options

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

Correct answer

A. $\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}$

Step-by-step solution

\begin{aligned} & F-m g=m a \\ & F=m a+m g \\ & F⁻(m-x) g=(m-x) 3 a \end{aligned}

Put F

\begin{aligned} & \mathrm{Ma}+\mathrm{mg}-\mathrm{mg}+\mathrm{xg}=3 \mathrm{ma}-3 \mathrm{xa} \\ & \mathrm{x}=\frac{2 \mathrm{ma}}{\mathrm{~g}+3 \mathrm{a}} \end{aligned}

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