A steel ball of radius 6 mm has a terminal speed of 12 cms − 1 in a viscous liquid. What will be the terminal speed of a steel ball of radius 3 mm in the same liquid?

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TestHub · Accepted Answer

The terminal velocity of a spherical body of radius $r$ in a viscous liquid is given by Stokes' law:

$v_{t} = \frac{2}{9} \frac{r ^{2} ( ρ - σ ) g}{η}$

Since the material of the ball and the liquid are the same, $v_{t} \propto r^{2}$ .

$\frac{v _{2}}{v _{1}} = (\frac{r _{2}}{r _{1}})^{2}$

Substituting the given values, $r_{1} = 6 mm$ , $v_{1} = 12 cms^{- 1}$ , and $r_{2} = 3 mm$ :

$\frac{v _{2}}{12} = (\frac{3}{6})^{2}$

$\frac{v _{2}}{12} = \frac{1}{4}$

$v_{2} = 3 cms^{- 1}$

Answer: $3 cms^{- 1}$

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