First slide

Viscosity

Question

If the terminal speed of a sphere of gold (density= 19.5 gm/cc) is 0.2 m/s in a viscous liquid (density= 1.5 gm/cc), find the terminal speed of a sphere of silver ( density = 10.5 gm/cc) of the same size in the same liquid.

Moderate

A

0.1 m/s
B

0.2 m/s
C

0.4 m/s
D

0.133 m/s

Solution

Terminal velocity $v_{r} = \frac{2}{9} \frac{r^{2} (ρ - σ) g}{η} \Rightarrow v_{r} \infty (ρ - σ) \frac{v_{r}}{0.2} = \frac{(10.5 - 1.5)}{(19.5 - 1.5)} = \frac{9}{18} = \frac{1}{2} \Rightarrow = 0.1 m / s .$

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