COMEDK · Physics · 5. Laws of Motion

A balloon with mass \(m\) is descending down with an acceleration \(a\) (where, \(a < g\) ). How much mass should be removed from it so that it starts moving up with an acceleration \(a\) ?

A \(\dfrac{m a}{g+a}\)
B \(\dfrac{m a}{g-a}\)
C \(\dfrac{2 m a}{g-a}\)
D \(\dfrac{2 m a}{g+a}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\dfrac{2 m a}{g+a}\)

Step-by-step Solution

Detailed explanation

Let \(F\) be the upward buoyant force acting on the balloon. When the balloon of mass \(m\) is descending with acceleration \(a\), the equation of motion is \(mg - F = ma\). From this, \(F = m(g - a)\). Let \(m'\) be the mass to be removed, so the new mass is \(m - m'\). When…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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