An air bubble of diameter 2 mm rises through a liquid of density 2000 kg·m⁻³ with a constant terminal speed of 0.5 cm·s⁻¹. Neglect the density of air and take g = 10 m·s⁻². What is the coefficient of viscosity of the liquid in poise?
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Question

An air bubble of diameter 2 mm rises through a liquid of density 2000 kg·m⁻³ with a constant terminal speed of 0.5 cm·s⁻¹. Neglect the density of air and take g = 10 m·s⁻². What is the coefficient of viscosity of the liquid in poise?

Options

G1 Physics · Accepted Answer

At terminal speed, the upward buoyant force is balanced by the viscous drag. For a small spherical bubble, using Stokes' drag: 6πηRv = (4 ÷ 3)πR³ρg. Cancel πR: 6ηv = (4 ÷ 3)R²ρg. Therefore, η = 2ρR²g ÷ (9v). Given, diameter = 2 mm, so R = 1 mm = 1×10⁻³ m. Also, ρ = 2000 kg·m⁻³, v = 0.5 cm·s⁻¹ = 5×10⁻³ m·s⁻¹. Thus, η = [2×2000×(10⁻³)²×10] ÷ [9×5×10⁻³] ≈ 0.889 Pa·s. Since 1 Pa·s = 10 poise, η ≈ 8.89 poise. The closest option is 8.8 poise. Correct option: B.