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 it starts moving up with an acceleration $a$?

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

Answer 1

Answer: (A)

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

Answer 2

Let F be the upthrust of the air. As the balloon is descending down with an acceleration a,
$\therefore mg=F=ma$ ... (i)

Let mass $m_0$ be removed from the balloon so that it starts moving up with an acceleration a. Then,
$F-(m-m_0)g=(m-m_0)a$
$F-mg+m_0g=ma-m_0a$ ... (ii)
Adding eqn. (i) and eqn. (ii), we get
$m_0g=2ma-m_0a$
$m_0g+m_0a=2ma$
$m_0(g+a)=2ma$
$m_0=\frac{2ma}{a+g}$