Question

A balloon with mass $M$ is decreasing down with an acceleration $a(a<g)$. What mass of its contents must be removed so that it starts moving up with same acceleration $a$?

• A. $\frac{2M\left(g\right)}{a}$
• B. $\frac{2M(g+a)}{g}$
• C. $\frac{Mg}{g+a}$
• D. $\frac{2Mg}{g+a}$

Answer 1

The correct option is D $\frac{2Mg}{g+a}$

Let, $F$ be the upthrust

So, $Mg-F=Ma$

Now, $m$ mass is removed

So, $F-(M-m)g=(M-m)a$

$or,Mg-Ma-(M-m)g=(M-m)a$ [Put $F = Mg + Ma]

$or,m=\frac{2mg}{g+a}$

Answer$:D$