Question

A balloon of mass 'M' is rising up with an acceleration 'a'. In order to triple its acceleration, the fraction of mass to be removed from the balloon is (\( g \) - acceleration due to gravity)

• A. \( \dfrac{a}{g+a} \)
• B. \( \dfrac{a}{g+2a} \)
• C. \( \dfrac{2a}{g+3a} \)
• D. \( \dfrac{2a}{g+2a} \)

Hint:

Use net force equations and substitute new conditions to find change in mass or acceleration.

Answer 1

The Correct Option is C

Initial: \( T - Mg = Ma \Rightarrow T = M(g+a) \)
New acceleration = 3a, new mass = \( M' \)
\( T = M'(g + 3a) \Rightarrow M(g+a) = M'(g + 3a) \Rightarrow \dfrac{M'}{M} = \dfrac{g+a}{g+3a} \)
Fraction removed = \( 1 - \dfrac{g+a}{g+3a} = \dfrac{(g+3a)-(g+a)}{g+3a} = \dfrac{2a}{g+3a} \)