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  4. The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m -3 at the rate of 0.35 cms -1. The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).

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Q. The diameter of an air bubble which was initially
$2 \,mm$, rises steadily through a solution of density $1750 \,kg \,m ^{-3}$ at the rate of $0.35 \, cms ^{-1}$. The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).

JEE MainJEE Main 2022Mechanical Properties of Fluids

Solution:

As the bubble is rising steadily the net force acting on it will be zero
image
(Because of density of air the value of mg can be neglected)
So $B=F \Rightarrow \frac{4 \pi}{3} R^3 \rho g=6 \pi \eta R v$
Putting $R =1 \,mm =10^{-3} m$
$\rho=1.75 \times 10^3\, kg / m ^3 $
$g =10 \,m / s ^2$
$v =0.35 \times 10^{-2}\, m / s $
$\eta=\frac{10}{9} \simeq 1 \cdot 11 \text { SI unit }=11 \text { poise }( CGS )$