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Question:

Three liquids of densities p1, p2 and p3 (with p1 > p2, p3) having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ1, θ2 and θ3 obey:

π/2 > θ1 > θ2 > θ3 ≥ 0

π > θ1 > θ2 > θ3 > π/2

π/2 < θ1 < θ2 < θ3 < π

0 ≤ θ1 < θ2 < θ3 < π/2

Solution:

Rise of a liquid in a capillary tube is given by , h = 2Tcosθ/(rρg) or cosθ = hrρg/(2T) where θ = angle of contact, r = radius of capillary tube, T = surface tension, ρ = density of liquid, now given that h, T and r are constants for all three liquids, and ρ1 > ρ2 > ρ3, therefore cosθ1 > cosθ2 > cosθ3 or θ1 < θ2 < θ3 now as the liquid is rising in all three capillaries therefore angles of contact will be acute, 0 ≤ θ1 < θ2 < θ3 < π/2