A sphere of radius 1 mm and density 500 kg/m³ is released inside a liquid of density 950 kg/m³ and viscosity 0.10 Pa·s. Take g = 10 m/s². If its upward terminal speed is N cm/s, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A sphere of radius 1 mm and density 500 kg/m³ is released inside a liquid of density 950 kg/m³ and viscosity 0.10 Pa·s. Take g = 10 m/s². If its upward terminal speed is N cm/s, find N.

G1 Physics · Accepted Answer

Because the sphere is lighter than the liquid, it rises. The magnitude of terminal speed is vₜ = 2r²(ρₗ−ρₛ)g/ (9η). Substitute: r = 10⁻³ m, ρₗ−ρₛ = 950−500 = 450 kg/m³, g = 10, η = 0.10. Therefore, vₜ = 2×10⁻⁶×450×10/ (9×0.10). The numerator is 0.009. The denominator is 0.9. Hence, vₜ = 0.01 m/s = 1 cm/s. Therefore, N = 1.