A spherical ball attains terminal velocity v while falling through a viscous fluid. It is replaced by another ball of the same mass but half the radius (made of denser material). Neglecting buoyancy, what is the new terminal velocity?

Correct answer: 2v

Solution

Neglecting buoyancy, terminal velocity comes from mg = 6*pi*eta*r*vₜ, so vₜ = mg/(6*pi*eta*r). With the mass held fixed, vₜ is inversely proportional to the radius, so halving r doubles the terminal velocity.

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