A balloon with its contents weighing $160N$ is moving down with an acceleration of $g/2{ms}^{-2}$. The mass to be removed from it so that the balloon moves up with an acceleration $g/3{ms}^{-2}$ is:

The correct option is D $10kg$
Initial Weight of balloon is 160 N (16kg)

first case

balloon moves down with an acceleration $\frac{g}{2}m{s}^{-2}$

Let constant force acting upward on the balloon is F

$160-F=16\times \frac{g}{2}$

$\Rightarrow F=80N$

Second case

Let final mass of the balloon is m

balloon moves upward due to force F with acceleration $\frac{g}{3}m{s}^{-2}$

$F-mg=m\frac{g}{3}$

$\Rightarrow F=\frac{4mg}{3}$

$\Rightarrow 80=\frac{4\times m\times 10}{3}$

$\Rightarrow m=6kg$

So, the mass removed from the balloon will be:

$m^{\prime }=16-6kg$

$m^{\prime }=10kg$

Correct option is B.