A sphere of density 5000 kg/m³ falls through liquid 1 having density 1000 kg/m³ and viscosity 1 Pa·s, and through liquid 2 having density 2000 kg/m³ and viscosity 0.50 Pa·s. If v₁/v₂ = N/3, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A sphere of density 5000 kg/m³ falls through liquid 1 having density 1000 kg/m³ and viscosity 1 Pa·s, and through liquid 2 having density 2000 kg/m³ and viscosity 0.50 Pa·s. If v₁/v₂ = N/3, find N.

Physics · Properties of solid and fluid · viscosity and terminal velocity

G1 Physics · Accepted Answer

For the same sphere, v₁/v₂ = η₂(ρₛ−ρ₁)/ [η₁(ρₛ−ρ₂)]. Substitute: η₁ = 1, η₂ = 0.50, ρₛ−ρ₁ = 5000−1000 = 4000, ρₛ−ρ₂ = 5000−2000 = 3000. Thus, v₁/v₂ = 0.50×4000/ [1×3000] = 2000/3000 = 2/3. Comparing with v₁/v₂ = N/3, we get N = 2.