An air bubble of diameter 6,mm rises steadily through a solution of density 1750,kg / m ^3 at rate o

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9-1.Fluid Mechanics

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An air bubble of diameter $6\,mm$ rises steadily through a solution of density $1750\,kg / m ^3$ at the rate of $0.35\,cm / s$. The co-efficient of viscosity of the solution (neglect density of air) is $..........\,Pas$ (given, $g =10\,ms ^{-2}$)

A

$5$

B

$10$

C

$8$

D

$9$

(JEE MAIN-2023)

Solution

Since the bubble is moving at constant speed the force acting on it is zero.

$B = F _{ V }$

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

$\eta=\frac{2 R ^2 \rho g }{9 v }=\frac{2 \times\left(3 \times 10^{-3}\right)^2 \times 1750 \times 10}{9 \times 0.35 \times 10^{-2}}=10\,Pas$

Standard 11

Physics

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