Question

Two liquids (say L₁ and L₂ ), having surface tensions T₁ and T₂ (where (T₁/T₂) = 2/3) and 2/3) and densities ρ₁ and ρ₂ (where (ρ₁/ρ₂) = 1/2), rise to the same height (say h) (above their respective outside levels) in identical (very small radius) capillary tubes. If their respective angles of contact, with the walls of the capillary tubes, are θ₁ and θ₂ , we would have

(1) 9cos²θ₂ - 16cos² θ₂ + 7 = 0

(2) 16sin²θ₂ - 9cos² θ₁ -7 = 0

(3) 9sin²θ₁ - 16sin² θ₂ -7 = 0

(4) 16sin²θ₁ - 9sin² -7 = 0

Answer 1

(4) 16sin²θ₁ - 9sin² -7 = 0

We know that

From the given data, we then have

∴ It is option (4) that is the correct choice.