A balloon with mass m is descending down with an acceleration a… | NEET 2014 (AIPMT)

Q16NEET 2014 · AIPMTMedium

Apparent Weight & Lift

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?

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Answer: (a)

Descending with $a$ : $mg - U = ma \Rightarrow U = m(g - a)$ , where $U$ is the upthrust (unchanged).
After removing $\Delta m$ , rising with $a$ : $U - (m - \Delta m)g = (m - \Delta m)a \Rightarrow m - \Delta m = \dfrac{m(g - a)}{g + a}$ .
$\Delta m = m - \dfrac{m(g-a)}{g+a} = \dfrac{2ma}{g + a}$
So the answer is (a) $\dfrac{2ma}{g+a}$ .

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