First slide

Viscosity

Question

A metal ball $B_{1}$ (density 3.2 g/cc) is dropped in water, while another metal ball $B_{2}$ (density 6.0 g/cc) is dropped in a liquid of density 1.6 g/cc.If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is

Moderate

A

2.0
B

0.5
C

4.0
D

indeterminate due to insufficient data

Solution

$v_{η} = v_{t 2}$
$\frac{2}{9} g \frac{r^{2}}{n_{w}} [σ_{1} - ρ_{w}] = \frac{2}{9} g \frac{r^{2}}{n_{1}} (σ_{2} - ρ_{l})$
$\Rightarrow \frac{n_{w}}{n_{l}} = \frac{σ_{1} - ρ_{w}}{σ_{2} - ρ_{l}} = \frac{3.2 - 1}{6 - 1.6} = \frac{1}{2}$

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