A small sphere of radius r falls from rest through a viscous liquid. At terminal velocity, the rate of heat generation by viscous drag is proportional to:
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Question

A small sphere of radius r falls from rest through a viscous liquid. At terminal velocity, the rate of heat generation by viscous drag is proportional to:

G1 Physics · Accepted Answer

Step 1: In Stokes flow, terminal speed vₜ = 2r²(ρs − ρl)g/(9η), so vₜ ∝ r². Step 2: The viscous drag at terminal speed is Fᵥ = 6πηrvₜ, so Fᵥ ∝ r × r² = r³. Step 3: Power converted to heat is P = Fᵥvₜ. Step 4: Thus P ∝ r³ × r² = r⁵. Final answer: r⁵ (Option A).