Question 130 of 130

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

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Answer: (A) $\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}$

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

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