If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 at a rate of 0.5 cm/s

Question

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 $kg / m^{3}$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take g = 10 $m / s^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(2)

$For constant speed: F_{B} = F_{v}$

$\Rightarrow ρ_{l} \frac{4}{3} π R^{3} g = 6 π η R v$

$\frac{2 ρ_{l} R^{2} g}{9 v} = η$

$\Rightarrow \frac{2}{9} \times \frac{2000 \times 10^{- 6} \times 10}{5 \times 10^{- 3}} = η$

$\Rightarrow η = \frac{80}{9} Poise = 8.88 Poise$

Solution

Q.
If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 $kg / m^{3}$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take g = 10 $m / s^{2}$ ) [2026]

1 0.88

2 8.8

3 88.8

4 0.088

Ans.
(2)

$For constant speed: F_{B} = F_{v}$

$\Rightarrow ρ_{l} \frac{4}{3} π R^{3} g = 6 π η R v$

$\frac{2 ρ_{l} R^{2} g}{9 v} = η$

$\Rightarrow \frac{2}{9} \times \frac{2000 \times 10^{- 6} \times 10}{5 \times 10^{- 3}} = η$

$\Rightarrow η = \frac{80}{9} Poise = 8.88 Poise$

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