Question

A balloon has a mass of $ 10 $ gram in air. The air escapes from the balloon at a uniform rate with a velocity of $ 5\, cm/s $ and the balloon shrinks completely in $ 2.5 \,s $ . The average force acting on the balloon will be

• A. 200 dyne
• B. 20 dyne
• C. 20 newton
• D. 2000 dyne

Answer 1

Answer: (B)

According to Newton's second law of motion,
$F =$ time rate of change of linear momentum
$= \frac{dp}{dt} = \frac{d}{dt} (mv)$
Since, here velocity $(v)$ is constant.
$\Rightarrow F = v \frac{dm}{dt}$
Here, $dm = 10 \,g, dt = 2.5 \,s$
$\Rightarrow F = \frac{5\times 10}{2.5} = 20\,g \,cm\,s$
$ = 20\,$ dyne