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)

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Navik GD 26 April 2025 Memory-Based Paper (Section I + II)
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  1. \(\frac{3 \mathrm{Ma}}{2 \mathrm{a}-\mathrm{g}}\)
  2. \(\frac{3 \mathrm{Ma}}{2 \mathrm{a}+\mathrm{g}}\)
  3. \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}\)
  4. \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}-\mathrm{g}}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}\)
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Detailed Solution

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Calcultion:

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F – mg = ma

F = ma + mg

F – (m – x)g = (m – x) 3a

Put F

Ma + mg – mg + xg = 3ma – 3xa

\(x=\frac{2 m a}{g+3 a}\)

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