First slide

Viscosity

Question

A ball of mass m and radius r is released in viscous liquid, The value of its terminal velocity is proportional to

Moderate

A

1 /r only
B

m/r
C

$(m / r)^{1 / 2}$
D

m only

Solution

we know that
$v_{T} = \frac{2}{9} \times \frac{r^{2} (ρ - σ)}{η} \times g = \frac{2}{9} \times \frac{(r^{3} ρ) (1 - σ / ρ) g}{rη} or v_{T} \propto (\frac{m}{r}) (∵ m \propto r^{3} ρ)$

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