First slide

Viscosity

Question

Two metal spheres are falling through a liquid of density $2 \times 10^{3} k g / m^{3}$ with the same terminal speed. The material density of sphere 1 and sphere 2 are $8 \times 10^{3} k g / m^{3} a n d 11 \times 10^{3} k g / m^{3}$ respectively. The ratio of their radii is:

Moderate

A

$\frac{11}{8}$
B

$\sqrt{\frac{11}{8}}$
C

$\frac{3}{2}$
D

$\sqrt{\frac{3}{2}}$

Solution

The terminal velocity of the spherical body of radius R, density $ρ$ falling through a liquid of density $σ$ is given by:
$υ_{T} = \frac{2}{9} \frac{R^{2} (ρ - σ) g}{η}$
or $\frac{{R_{1}}^{2}}{{R_{2}}^{2}} = \frac{ρ_{2} - σ}{ρ_{1} - σ}$
Substituting the given values, we get;
$\begin{array}{l} \frac{{R_{1}}^{2}}{{R_{2}}^{2}} = \frac{(11 \times 10^{3} - 2 \times 10^{3})}{(8 \times 10^{3} - 2 \times 10^{3})} = \frac{9}{6} = \frac{3}{2} \\ \frac{R_{1}}{R_{2}} = \sqrt{\frac{3}{2}} \end{array}$

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