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

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Fluid Mechanics

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}

)

Answer: 10

Solution

Since the bubble rises at constant velocity, the net force is zero. The buoyant force equals the viscous drag force:

\frac{4}{3} π R^{3} ρ g = 6 π η R v

Solving for viscosity:

η = \frac{2 R ^{2} ρ g}{9 v} = \frac{2 \times ( 3 \times 1 0 ^{- 3} ) ^{2} \times 1750 \times 10}{9 \times 0.35 \times 1 0 ^{- 2}} = 10 Pa\cdots

JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Integer answer

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