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Let upthrust of air be Fa. For downward motion of balloon, Fa = mg - ma ⇒ Fa = m(g - a). For upward motion, Fa - (m - Δm)g = (m - Δm)a. From these equations, determine Δm.

1. Δm = 2ma / (g + a)
2. Δm = ma / (g - a)
3. Δm = ma / (g + a)
4. Δm = 2ma / (g - a)

Correct answer: Δm = ma / (g + a)

Solution

To find Δm, equate the upthrust Fa from both equations. Simplifying the resulting equation gives Δm = ma / (g + a).

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