A balloon of gross weight $W$ newton descends with an acceleration $f m / s^{2}$ . The weight that must be thrown out in order to give balloon an equal upward acceleration will be

W f / g

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2 W f / g

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2 W f / (g + f)

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W (g + f) / f

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Solution

The correct option is C $2 W f / (g + f)$
Where balloon is going down,(assuming positive y-axis to be positive)
Let $M =$ mass of balloon [Ref, image 1]
$g =$ 10m/s^2$
For going down,
$R - M g = - M F$
$R = M (g - F)$ ...(1)
after throwing weight
$\Rightarrow R - (M - m) g - (M - m) F$ [Ref. image 2]
$R = (M - m) (g + F)$ ...(2)
$M g - M F = M g + M F - m g - m F$
$m (g + F) = 2 M F$
$m = \frac{2 M F}{g + F}$
Hence, option $(C)$ is correct answer.
Hence, option $(C)$ is correct answer.

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A balloon of gross weight W newton descends with an acceleration f m/s2. The weight that must be thrown out in order to give balloon an equal upward acceleration will be

A balloon of gross weight $W$ newton descends with an acceleration $f m / s^{2}$ . The weight that must be thrown out in order to give balloon an equal upward acceleration will be