A small sphere falls from rest through a viscous liquid. At terminal speed, viscous dissipation produces heat. Find how the rate of heat production depends on sphere radius r.
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A small sphere falls from rest through a viscous liquid. At terminal speed, viscous dissipation produces heat. Find how the rate of heat production depends on sphere radius r.

G1 Physics · Accepted Answer

Step 1: Use viscous-force relations: shear F = ηA(dv/dy), Stokes force 6πηrv, or Reynolds number Re = ρvD/η as appropriate. Step 2: At terminal speed set net weight/buoyancy equal to viscous drag and use the given geometry. Applying these relations to the given data gives A: dQ/dt ∝ r⁵. Final answer: A.