A sphere of mass M and radius R falls through a viscous fluid. Under Stokes' law, ignoring the effect of buoyancy, the terminal speed is proportional to:
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Question

A sphere of mass M and radius R falls through a viscous fluid. Under Stokes' law, ignoring the effect of buoyancy, the terminal speed is proportional to:

G1 Physics · Accepted Answer

Step 1: At terminal speed, gravitational force balances viscous resistance. Step 2: Stokes' drag on a sphere is Fᵥ = 6πηRvₜ. Step 3: Ignoring buoyancy as implicit in the listed options, Mg = 6πηRvₜ. Step 4: Rearranging, vₜ = Mg/(6πηR). Step 5: For fixed g and viscosity η, vₜ ∝ M/R. Final answer: M/R (Option B). Note: including buoyancy gives (M − ρfluid·4πR³/3)g/(6πηR).