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Question

Three liquids having densities ρ1, ρ2 and ρ 3 ( ρ1>ρ2>ρ3), having the same value of surface tension T, rise to the same height h in three identical capillaries. The angle of contact θ1, θ2 and θ3 obeys

A
π2>θ1>θ2>θ30
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B
0θ1<θ2<θ3<π2
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C
π2<θ1<θ2<θ3<π
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D
π>θ1>θ2>θ3>π2
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Solution

The correct option is B 0θ1<θ2<θ3<π2
We know capillary rise,
h=2Tcosθrρg


Liquid is rising in capillary tube, so angle of contact is 0 θ<π2.
For the constant value of surface tension T and radius of capillary r of a fluid.
hcosθρ
Since, h1=h2=h3
cosθ1ρ1=cos θ2ρ2=cos θ3ρ3 .....(1)
Given, ρ1>ρ2>ρ3
Hence, to maintain the equal ratio in (1),
cosθ1>cosθ2>cosθ3
θ1<θ2<θ3
[ as the value of angle increases from 0 to π2, the value of cosθ decreases from 1 to 0 ]
Hence, 0θ1<θ2<θ3<π2

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