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Question

A balloon of mass M descends with an acceleration a0 The mass that must be thrown out in order to give the balloon an equal upward acceleration will be

A
Ma0g
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B
2Ma0g
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C
2Ma0g+a0
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D
M(g+a0)a0
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Solution

The correct option is B 2Ma0g+a0
When the balloon descends with acceleration ao, total downward force is equal to Mao.
Mao=net downward force = weight of balloon - buoyant force
Mao=MgVbρag.....(I)
Now lets say m mass is removed from the balloon, due to which the balloon rises with ao, So the net upward force this time is equal to (Mm)ao
(Mm)ao= net upward force = buoyant force- net weight of balloon
(Mm)ao=Vbρag(Mm)g.....(II)
adding (I) and (I), we have
2Maomao=mg2Mao=mg+mao=m(g+ao)m=2Mao(g+ao)

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