A balloon of mass m is descending down with an acceleration frac{g}{2} . How much m

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4-1.Newton's Laws of Motion

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A balloon of mass $m$ is descending down with an acceleration $\frac{g}{2}$. How much mass should be removed from it so that it starts moving up with same acceleration?

A

$\frac{{2\,m}}{3}$

B

$\frac{{m}}{3}$

C

$3\,m$

D

$\frac{4}{3}\,m$

Solution

$\Rightarrow m g-F=\frac{m g}{2}$

$F=\frac{m g}{2}$ $…(1)$

$\mathrm{F}-\left(\mathrm{m}-\mathrm{m}_{1}\right) \mathrm{g}=\left(\mathrm{m}-\mathrm{m}_{1}\right) \mathrm{g} / 2$

$\mathrm{F}=\frac{3}{2}\left(\mathrm{m}-\mathrm{m}_{1}\right) \mathrm{g}$ $…(2)$

By equation $( 1 )$ and $( 2 )$

$\begin{aligned} \frac{m g}{2} &=\frac{3}{2}\left(m-m_{1}\right) g \\ m &=3 m-3 m_{1} \\ 3 m_{1} &=2 m \\ m_{1} &=\frac{2 m}{3} \end{aligned}$

Standard 11

Physics

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