A spherical body of diameter D falls in a viscous medium. Its Stokes-law terminal speed vₜ is proportional to:
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Question

A spherical body of diameter D falls in a viscous medium. Its Stokes-law terminal speed vₜ is proportional to:

G1 Physics · Accepted Answer

Step 1: Weight minus buoyancy = viscous drag at terminal speed. Step 2: (4/3)πr³(ρₛ − ρₗ)g = 6πηrvₜ. Step 3: Rearranging, vₜ = 2r²(ρₛ − ρₗ)g/(9η). Step 4: For fixed densities and viscosity, vₜ ∝ r². Since D = 2r, vₜ ∝ D². Final answer: D² (Option C).