First slide

Viscosity

Question

If the terminal speed of a sphere of gold (density $= 19 \cdot 5 kg / m^{3})$ is 0.2m/ s in viscous liquid (density $= 1 \cdot 5 kg / m^{3})$ find the terminal speed of a sphere of silver (density = 10.5kg/m³) of the same size in the same liquid

Moderate

A

0.4m /s
B

1.33m / s
C

0.1m/s
D

0.2 m/s

Solution

we know that
$V_{T} = \frac{2}{9} \frac{r^{2} (ρ - σ) g}{η} in the present case \frac{{(v_{T})}_{Ag}}{{(v_{T})}_{Au}} = \frac{ρ_{Ag} - σ_{l}}{ρ_{Au} - σ_{l}} ∴ {(v_{T})}_{Ag} = {(v_{T})}_{Au} \times (\frac{ρ_{Ag} - σ_{l}}{ρ_{Au} - σ_{l}}) = 0 \cdot 2 \times \frac{(10 \cdot 5 - 1 \cdot 5)}{(19 \cdot 5 - 1 \cdot 5)} = 0 \cdot 2 \times (\frac{9}{18}) = 0 \cdot 2 \times (\frac{1}{2}) = 0 \cdot 1 m / s$

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