A solid steel ball of diameter 3.6 mm reaches terminal speed 2.45×10⁻² m/s while falling through oil of density 925 kg/m³. The density of steel is 7825 kg/m³ and g = 9.8 m/s². The viscosity of the oil is:
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Question

A solid steel ball of diameter 3.6 mm reaches terminal speed 2.45×10⁻² m/s while falling through oil of density 925 kg/m³. The density of steel is 7825 kg/m³ and g = 9.8 m/s². The viscosity of the oil is:

Options

G1 Physics · Accepted Answer

For a sphere falling at terminal speed in a viscous fluid, Stokes' law gives v t v_t v t ​ = [2R²g(ρ_s-ρ_f)]/(9η). Therefore, η = [2R²g(ρ_s-ρ_f)]/(9 v t ) . v_t). v t ​ ) . Radius: R = 3.6/2 mm = 1.8×10⁻³ m. Density difference: ρ_s-ρ_f = 7825-925 = 6900 kg/m³. Substitute: η = [2(1.8×10⁻³)²(9.8)(6900)]/[9(2.45×10⁻²)] ≈ 1.99 Pa·s. Correct option: D.