A small sphere is released from rest and sinks through a viscous liquid. Friction with the liquid generates heat. When the sphere is moving at its terminal velocity, how does the rate at which heat is produced depend on the sphere's radius r?

proportional to r
proportional to r²
proportional to r³
proportional to r⁵
proportional to 1/r

Correct answer: proportional to r⁵

Solution

At terminal velocity all gravitational power input is converted to heat: P = (net weight) * vₜ. Net weight scales as r³ and Stokes terminal velocity as r².

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