A metal ball A (density 3.2 g/cc) is dropped in water, while another metal ball B (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

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0.25

2.0

0.5

4.0

answer is B.

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Detailed Solution

Terminal velocity is given by

$v_{T} = \frac{2}{9} \frac{r^{2} (ρ_{1} - ρ_{2}) g}{η}$

$\Rightarrow {(v_{T})}_{A} = \frac{2}{9} \frac{r^{2} (32 - 1) g}{η_{w}}$ and ${(v_{T})}_{B} = \frac{2}{9} \frac{r^{2} (6.0 - 1.6) g}{η_{I}}$

$Given, {(v_{T})}_{A} = {(v_{T})}_{B}$

Equating these two we get $\frac{η_{ω}}{η_{l}} = 0.5$

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