[0 \leq \theta_1 < \theta...] Three liquids of densities ρ1, ρ2 and ρ3 (with ρ1

For Competitive Exams

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 contact θ₁, θ₂ and θ₃ obey

$\pi > \theta_1 > \theta_2 > \theta_3 > \dfrac{\pi}{2}$

$\dfrac{\pi}{2}> \theta_1 > \theta_2 > \theta_3 \geq 0$

$0 \leq \theta_1 < \theta_2 < \theta_3 < \dfrac{\pi}{2}$

$\dfrac{\pi} \theta_1 < \theta_2 < \theta_3 < \pi$

Explanation:

$h = \dfrac{2T\cos \theta}{\rho gr}$

$\dfrac{\cos \theta_1}{\rho_1}= \dfrac{\cos \theta_2}{\rho_2}= \dfrac{\cos \theta_3}{\rho_3}$

$\cos \theta_1 > \cos \theta_2 > \cos \theta_3 \ as\ \rho_1 > = \rho_2 > \rho_3$

$0 \leq \theta_1 < \theta_2 < \theta_3 < \dfrac{\pi}{2}$

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