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 - 1 . The co-efficient of viscosity of the solution (neglect density of air) is ___

Question

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 - 1 . The co-efficient of viscosity of the solution (neglect density of air) is ________ Pas (given, g = 10 m s - 2 ).

TestHub · Accepted Answer

The bubble is moving with a constant velocity so the net force acting on the body is zero.
Stokes' law defines the drag force which is given by $F = 6 π η r v$
The buoyant force is given by $B = V ρ g = \frac{4}{3} π r^{3} ρ g$
Hence, it can be written that
$\frac{4}{3} π r^{3} ρ g = 6 π η r v \Rightarrow η = \frac{2 r^{2} ρ g}{9 v} = \frac{2 \times {(3 \times 10^{- 3})}^{2} \times 1750 \times 10}{9 \times 0.35 \times 10^{- 2}} = 10 Pas$

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