Question

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 is starts moving up with an acceleration ${}^{\prime }{a}^{\prime }$?

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

Answer 1

The correct option is A $\frac{2ma}{g+a}$

$mg-F=ma$ .... (1)
$F-(m-m^{\prime })g=(m-m^{\prime })a$
from (1)
$F-mg+m^{\prime }g=ma-m^{\prime }amg-ma-mg+m^{\prime }g=ma-m^{\prime }a$
$m^{\prime }(g+a)=2ma$
$m^{\prime }=\frac{2ma}{g+a}$