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
$\frac{2 ma}{g + a}$
B
$\frac{2 ma}{g - a}$
C
$\frac{ma}{g + a}$
D
$\frac{ma}{g - a}$

Solution:

Forces acting on balloon are its weight and buoyant force (B). The buoyant force will be constant as there is no charge in volume of the balloon.
When balloon is descending down

mg - B = ma------------(i)

When balloon is moving up

$B - (m - m_{0}) g = (m - m_{0}) a (ii)$

Balloon is moving down Balloon is moving up

Equation (i) + Equation (ii)

$\Rightarrow mg - mg + m_{0} g = ma + ma = m_{0} a$

$\Rightarrow m_{0} = \frac{2 ma}{g + a}$

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?

Solution:

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