Question

A hot air balloon of mass m is descending vertically with downward acceleration a. The amount of mass that must be thrown out to give the balloon an upward acceleration a is?

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

Answer 1

Answer: (B)

$\frac{2ma}{g+a}$

Let the thrust on the balloon is R.
Initially, $mg-R=ma$
Let a mass $\Delta$m is removed from the balloon, so that it rises up with same acceleration a
$(m-\Delta m)g$
$R-(m-\Delta m)g=(m-\Delta m)a$
$\Rightarrow R-mg+\Delta mg=ma-\Delta ma$
$\Rightarrow -ma+\Delta mg=ma-\Delta ma$
$\Rightarrow \Delta m(g+a)=2ma$
$\Delta m=\frac{2ma}{(g+a)}$.