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An air bubble...

Question

An air bubble of radius 1 mm moves up with uniform velocity of 0.109 ms $^{- 1}$ in a liquid column of density 14.7 x 10 $^{3}$ kg/m $^{3}$ , the coefficient of viscosity will be (g = 10ms $^{- 2}$ ) $ρ_{a i r}$ = 1.3 kg/m $^{3}$

0.3 Pa - s

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300 Pa - s

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15 Pa - s

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150 Pa - s

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Solution

The correct option is A 0.3 Pa - s
Given, $r = 1 m m = 0.001 m$
$ρ = 14.7 \times 10^{3} k g / m^{3}$
$v = 0.109 m s^{- 1}$

Frictional force upwards due to liquid = Buoyant force
$6 π η r v = V ρ g$

$η = \frac{V ρ g}{6 π r v}$

$η = 0.3$ Pa-s

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