First slide

Newton's laws of motion

Question

A balloon of mass M is descending at a constant acceleration a. When a mass m is released from the balloon, it starts rising with the same acceleration a. Assuming that its
volume does not change, what is the value of m?

Moderate

A

$\frac{a}{a + g} M$
B

$\frac{2 a}{a + g} M$
C

$\frac{a + g}{a} M$
D

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

Solution

Suppose F= upthrust due to buoyancy
Then while descending, we find
$M g - F = M a$ …..(i)
When ascending, we have
$F - (M - m) g = (M - m) a$ …….(ii)
Solving Eqs. (i) and (ii), we get $m = [\frac{2 a}{a + g}] M$

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