Question

A hydrogen gas filled balloon having a mass of 25g is released up in the air . As the balloon ascends , the gas starts leaking fro it with a uniform velocity of 12cm/s as a result , the balloon shrinks completely in 5s . Find the average force acting on the balloon.

Answer 1

Dear Student,
$$\begin{gathered} Theballoonloses25gor0.025kggasin5s \\ sorateofflowofgas,\frac{dm}{dt}=0.025/5=0.005kg/s \\ Velocityofthegas,v=12cm/s=0.12m/s \\ Now,rateofchangeofmomentumis, \\ \frac{dp}{dt}=\frac{d\left(mv\right)}{dt} \\ \Rightarrow F=v\frac{dm}{dt}+m\frac{dv}{dt} \\ \Rightarrow F=v\frac{dm}{dt}+0 \\ \Rightarrow F=0.12(0.005)=0.0006N \end{gathered}$$
Regard