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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
$\frac{2ma}{g + a}$
B
$\frac{2ma}{g - a}$
C
$\frac{ma}{g + a}$
D
$\frac{ma}{g - a}$
Detailed Solution
Let the upthrust of air be $F_a$.
Downward motion: $mg - F_a = ma$
Upward motion after removing $\Delta m$: $F_a - (m - \Delta m)g = (m - \Delta m)a$
Solving, $\Delta m = \frac{2ma}{g + a}$
Downward motion: $mg - F_a = ma$
Upward motion after removing $\Delta m$: $F_a - (m - \Delta m)g = (m - \Delta m)a$
Solving, $\Delta m = \frac{2ma}{g + a}$