A gold sphere (density 19.5 g/cm³) falls through a viscous liquid (density 1.5 g/cm³) with terminal speed 0.2 m/s. Find the terminal speed of a silver sphere (density 10.5 g/cm³) of the same radius in the same liquid.

0.1 m/s
0.133 m/s
0.2 m/s
0.4 m/s

Correct answer: 0.1 m/s

Solution

For a sphere falling in a viscous fluid, terminal velocity v = (2/9)*(r² * g / eta)*(rho_sphere - rho_liquid). With same radius, liquid, and g, v is proportional to (rho_sphere - rho_liquid). Taking the ratio of silver to gold gives the new terminal speed.

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