JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Laws of Motion

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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)

(A) $\frac{3 M a}{2 a - g}$
(B) $\frac{3 Ma}{2 a + g}$
(C) $\frac{2 Ma}{3 a + g}$ ✓ Correct
(D) $\frac{2 Ma}{3 a - g}$

Answer: (C)

Solution

Let

F

be the (constant) upward buoyant/lift force on the balloon, unchanged before and after mass is released.

Before release, total mass

M

accelerates upward at

a

F - M g = M a ⟹ F = M (a + g)

After a mass

x

is released, the remaining mass

M - x

accelerates upward at

3 a

F - (M - x) g = (M - x) (3 a)

Substitute

F = M (a + g)

M (a + g) - (M - x) g = 3 a (M - x)

M a + M g - M g + xg = 3 a M - 3 a x

M a + xg = 3 a M - 3 a x

x (g + 3 a) = 2 a M

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

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Laws of Motion

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