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Question

If a balloon of mass $$M$$ is descending down with an acceleration $$a( < g)$$, then what is the value of mass $$m$$ (of its contents) that must be removed so that it starts moving up with an acceleration $$a$$?


A
Ma(g+a)
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B
2Ma(g+a)
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C
M(g+a)
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D
Not possible
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Solution

The correct option is A $$\dfrac {2Ma}{(g + a)}$$
Let the retarding force acting on the balloon in vertically upward direction be $$F$$. When the balloon is descending down with acceleration $$a$$, its equation of motion can be given
as $$Ma = Mg - F$$
or $$F = Mg - Ma .... (i)$$
Let $$M$$ mass is removed from the balloon. When it moves up with acceleration $$a$$, its equation of motion can be given as
$$(M - m) a = F - (M - m)g$$
From Eq. (i)
$$Ma - ma = Mg - Ma - Mg + mg$$
$$\Rightarrow m = \dfrac {2Ma}{(g + a)}$$.
713960_679130_ans_e57c2615887042218f25f63cfb1028cf.png

Physics

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