Three liquids of densities $\rho $1, $\rho $2 and $\rho $3 (with $\rho $1 > $\rho $2 > $\rho $3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $\theta $1, $\theta $2 and $\theta $3 obey

Question

Three liquids of densities $\rho $₁, $\rho $₂ and $\rho $₃ (with $\rho $₁ > $\rho $₂ > $\rho $₃), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $\theta $₁, $\theta $₂ and $\theta $₃ obey

${\pi \over 2} > {\theta _1} > {\theta _2} > {\theta _3} \ge 0$

0 $ \le $ $\theta $₁ < $\theta $₂ < $\theta $₃ < ${\pi \over 2}$

${\pi \over 2} < {\theta _1} < {\theta _2} < {\theta _3} < \pi $

$\pi > {\theta _1} > {\theta _2} > {\theta _3} > {\pi \over 2}$

Solution

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