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Question 41

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 '3a' will be (Take ' g ' as acceleration due to gravity)

Solution

Initially: F_buoy - Mg = Ma, so F_buoy = M(g+a).

After releasing mass m: F_buoy - (M-m)g = (M-m)(3a).

M(g+a) = (M-m)(g+3a), M(g+a) = M(g+3a) - m(g+3a)

m(g+3a) = M(g+3a-g-a) = 2Ma, m = 2Ma/(g+3a).

The correct answer is Option 1.

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