A balloon with its contents weighing 160 N is moving down with an acceleration of $\text{g/2}{\text{ms}}^{-2}$ . The mass to be removed from it so that the balloon moves up with an acceleration of $\text{g/3}{\text{ms}}^{-2}$ is $\left(\text{g}=\text{10}{\text{ms}}^{-2}\right)$

$160-{\text{F}}_{\text{B}}=16.\frac{\text{g}}{\text{2}}$

${\text{F}}_{\text{B}}=160-8\times 10$

${\text{F}}_{\text{B}}=160-80$

${\text{F}}_{\text{B}}=80$

${\text{F}}_{\text{B}}-\left(16-\text{m}\right)\text{g}=\left(16-\text{m}\right)\text{g/3}$

$\text{80}-\left(16-\text{m}\right)\text{g}=\left(16-\text{m}\right)\text{g/3}$

$80=16-\text{m}\left(3\text{g}+\text{g/3}\right)$

$=\left(16-\text{m}\right)\frac{\left(\text{4g}\right)}{\text{3}}$

$80=\frac{64\text{g}-4\text{mg}}{3}$

$240=64\times 10-4\text{mg}$

$\text{240}-\text{640}=-\text{4mg}$

$-\text{400}=-4\text{mg}$

$-\text{100}=-\text{mg}$

$\frac{100}{10}=\text{m}$

$\text{10}=\text{m}$

$\text{m}=\text{10}\text{kg}$