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

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)
  1. $\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}$
  2. $\frac{3 \mathrm{Ma}}{2 \mathrm{a}-\mathrm{g}}$
  3. $\frac{3 \mathrm{Ma}}{2 \mathrm{a}+\mathrm{g}}$
  4. $\frac{2 \mathrm{Ma}}{3 \mathrm{a}-\mathrm{g}}$

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

Asked in: JEE Main 2025 (28 Jan Shift 2)

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