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)

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, $F-(m-m_0)g=(m-m_0)a$
$F-mg+m_{0}g=ma-m_{0}a$ ... (ii)
Adding eqn. (i) and eqn. (ii), we get
$m_{0}g=2ma-m_{0}a$
$m_{0}g+m_{0}a=2ma$
$m_0(g+a)=2ma$
$m_0=\frac{2ma}{a+g}$