Question

A balloon of mass ' $M$ ' descends with an acceleration ' $a$ ' , $(< g)$. What mass need to be removed from the balloon so that it starts ascending with acceleration ' $a$ '?

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

Answer 1

Answer: (B)

The given situation is shown in the figure

In above figures, $M$ is the mass of balloon and $M'$ is the mass remove from the balloon.
According to Newton's law of motion in first case,
$M g-F=M a \Rightarrow F=M g-M a \ldots$ (i)
According to Newton's second law of motion, for second case,
$F-\left(M-M'\right) g=\left(M-M'\right) a$
$\Rightarrow F-M g +M' g=M a-M' a$
$\Rightarrow M g-M a-M g +M' g=M a-M^{\prime} a$
[ from Eq. (i)]
$\Rightarrow M' g +M'a=M a +M a$
$\Rightarrow M'(g +a)=2 M a$
$\Rightarrow M'=\frac{2 M a}{g +a}$