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

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 givenas $$Ma = Mg - F$$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)$$Ma - ma = Mg - Ma - Mg + mg$$$$\Rightarrow m = \dfrac {2Ma}{(g + a)}$$.Physics

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