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.

Answer 1

formula of height of liquid in capillary tube is given by, $h=\frac{2Tcos\theta}{\rho rg}$

where, T is surface tension, $\theta$ is angle of contact , $\rho$ is density and r is radius of capillary tube.

according to question,

T = constant [ same surface tension ]

r = constant [ identical capillaries ]

h = constant [ same height ]

g always remains constant..

so, $cos\theta\propto\rho$

here given,

$\rho_1 > \rho_2 > \rho_3$

so, $cos\theta_1 > cos\theta_2 > cos\theta_3$

as we know, cosine is decreasing function within 0 to π/2.

so, $\theta_3 > \theta_2 > \theta_1$

and it is also written as

$\frac{\pi}{2} > \theta_3 > \theta_2 > \theta_1 > 0$