A solid sphere of radius 1 mm and density 5500 kg/m³ falls through a liquid of density 1000 kg/m³ and viscosity 1 Pa·s. Take g = 10 m/s². If its terminal speed is N cm/s, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A solid sphere of radius 1 mm and density 5500 kg/m³ falls through a liquid of density 1000 kg/m³ and viscosity 1 Pa·s. Take g = 10 m/s². If its terminal speed is N cm/s, find N.

G1 Physics · Accepted Answer

Terminal speed is vₜ = 2r²(ρₛ−ρₗ)g/ (9η). Substitute: r = 1 mm = 10⁻³ m, ρₛ−ρₗ = 5500−1000 = 4500 kg/m³, g = 10 m/s², η = 1 Pa·s. Thus, vₜ = 2×10⁻⁶×4500×10/9. The numerator is 0.09. Therefore, vₜ = 0.01 m/s = 1 cm/s. Hence, N = 1.