A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity v₀. Estimated maximum error in the quantity η is :
(Ignore errors associated with σ, ρ and g, gravitational acceleration)

Question

A spherical body of radius r and density σ falls freely through a viscous liquid having density ρ and viscosity η and attains a terminal velocity v₀. Estimated maximum error in the quantity η is :

(Ignore errors associated with σ, ρ and g, gravitational acceleration)

G1 Physics · Accepted Answer

For a sphere falling with terminal velocity in a viscous liquid, Stokes' law gives v₀ = 2r²g(σ - ρ)/(9η). Rearrange for viscosity: η = 2r²g(σ - ρ)/(9v₀). Ignoring errors in σ, ρ and g, η ∝ r²/v₀. For maximum fractional error, the magnitudes of the fractional contributions are added: Δη/η = 2Δr/r + Δv₀/v₀. Correct option: B.