Liquids with densities ρ₁ ρ₂ ρ₃ have equal surface tension T and rise to the same height in three identical capillaries. How are their contact angles θ₁, θ₂ and θ₃ ordered?

Question

Liquids with densities ρ₁ > ρ₂ > ρ₃ have equal surface tension T and rise to the same height in three identical capillaries. How are their contact angles θ₁, θ₂ and θ₃ ordered?

G1 Physics · Accepted Answer

Step 1: For capillary rise, h = 2T cosθ/(ρgr). Step 2: The three capillaries have the same h, r, T, and g. Step 3: Rearrange: cosθ = hρgr/(2T), so cosθ ∝ ρ. Step 4: ρ₁ > ρ₂ > ρ₃ gives cosθ₁ > cosθ₂ > cosθ₃. Step 5: Cosine decreases as θ increases between 0 and π/2, so θ₁ < θ₂ < θ₃. Final answer: 0 ≤ θ₁ < θ₂ < θ₃ < π/2 (Option D).