A ballon and its content having mass M is moving up with 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) [2025]

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Solution

Q.
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) [2025]

1 $\frac{3 M a}{2 a - g}$

2 $\frac{3 M a}{2 a + g}$

3 $\frac{2 M a}{3 a + g}$

4 $\frac{2 M a}{3 a - g}$

Ans.
(3)

$F - M g = M a \Rightarrow F = M a + M g$ ... (i)

$F - (M - x) g = (M - x) 3 a$ ... (ii)

From (i) and (ii)

$M a + M g - M g + x g = 3 M a - 3 x a \Rightarrow x = \frac{2 M a}{g + 3 a}$

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