A solid sphere of density 4500 kg/m³ and radius 1 mm moves in a liquid of viscosity 1 Pa·s. In the simple Stokes model, if its time constant is N ms, find N.

Question

G1 Physics · Accepted Answer

The Stokes time constant is τ = m/(6πηr). For a sphere, m = (4πr³/3)ρₛ. Therefore, τ = [(4πr³/3)ρₛ]/ (6πηr) = 2ρₛr²/(9η). Substitute: ρₛ = 4500 kg/m³, r = 10⁻³ m, η = 1 Pa·s. Thus, τ = 2×4500×10⁻⁶/9 = 10⁻³ s = 1 ms. Hence, N = 1.