Same-radius spherical balls of different densities σ fall through a liquid of density ρ. Which plot correctly shows their terminal velocity v versus density ratio σ/ρ? Image (four plots)
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Question

Same-radius spherical balls of different densities σ fall through a liquid of density ρ. Which plot correctly shows their terminal velocity v versus density ratio σ/ρ? Image (four plots)

G1 Physics · Accepted Answer

Step 1: At terminal velocity, viscous drag balances effective weight: 6πηrv = (4/3)πr³(σ − ρ)g. Step 2: Rearranging, v = 2r²g(σ − ρ)/(9η). Step 3: Write σ − ρ = ρ(σ/ρ − 1). Step 4: With r, ρ and η fixed, v ∝ (σ/ρ − 1): a straight line crossing zero at σ/ρ = 1, in the settling region σ > ρ. Final answer: Graph 1 (Option A).