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Q.

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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a

0.25

b

2.0

c

0.5

d

4.0

answer is B.

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Detailed Solution

Terminal velocity is given by

vT=29r2ρ1−ρ2gη

⇒vTA=29r2(32−1)gηw and  vTB=29r2(6.0−1.6)gηI

 Given, vTA=vTB

Equating these two we get ηωηl=0.5

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