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 angles of contactθ1,θ2 and θ3 obey
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a
π2>θ1>θ2>θ3≥0
b
0≤θ1<θ2<θ3<π2
c
π2<θ1<θ2<θ3<π
d
π>θ1>θ2>θ3>π2
answer is B.
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Detailed Solution
Capillary rise, h=2Tcosθρgr For given value of T and r,h∝cosθρAlso, h1=h2=h3 or, cosθ1ρ1=cosθ2ρ2=cosθ3ρ3 Since, ρ1>ρ2>ρ3, so cosθ1>cosθ2>cosθ3 For 0≤θ<π2,θ1<θ2<θ3 Hence, 0≤θ1<θ2<θ3<π2