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STD 11 - 9.1 , fluid mechanics — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 9.1 , fluid mechanics4 Marks
Question
The diameter of an air bubble which was initially $2\,mm$, rises steadily through a solution of density $1750\,kg\,m\,m ^{-3}$ 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).
✓

Answer

b
As the bubble is rising steadily the net force acting on it will be zero

(Because of density of air the value of mg can be neglected)

So $B = F \Rightarrow \frac{4 \pi}{3} R ^{3} \rho g =6 \pi \eta Rv$

Putting $R =1\,mm =10^{-3}\,m$

$\rho=1.75 \times 10^{3}\,kg / m ^{3}$

$g =10\,m / s ^{2}$

$v =0.35 \times 10^{-2}\,m / s$

$\eta=\frac{10}{9}=1.11$ SI unit $=11$ poise $( CGS )$

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