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Q.

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

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a

π2<θ1<θ2<θ3<π

b

π>θ1>θ2>θ3>π2

c

π2>θ1>θ2>θ3≥0

d

0≤θ1<θ2<θ3<π2

answer is D.

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Detailed Solution

h=2Tcos⁡θρgr⇒cos⁡θρ= constant ρ1>ρ2>ρ3so cos⁡θ1>cos⁡θ2>cos⁡θ3θ1<θ2<θ3Liquid rises so constants angles are acute.0<θ1<θ2<θ3<π/2
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Three liquids of densities ρ1, ρ2 and ρ3 (with ρ1>ρ2>ρ3, having the same value of surface tension T, rise to the same height in three identical capillaries. The angle of contact θ1,θ2 and θ3 obey :