Laws of Motion - Result Question 24
24. 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’?
[2014]
(a) $\frac{2 m a}{g+a}$
(b) $\frac{2 ma}{g-a}$
(c) $\frac{ma}{g+a}$
(d) $\frac{ma}{g-a}$
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Answer:
Correct Answer: 24. (a)
Solution:
- (a) Let upthrust of air be $F_a$ then For downward motion of balloon,
$F_a=mg-ma \Rightarrow F a=m(g-a)$
For upward motion,
$ \begin{equation*} F_a-(m-\Delta m) g=(m-\Delta m) a \tag{ii} \end{equation*} $
From equation (i) and (ii),
Therefore, $\Delta m=\frac{2 m a}{(g+a)}$
