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

Solution :
According to ascent formula for capillary tube, $$h = \frac{{2T\cos \theta }}{{\rho gr}}$$
$$\therefore \frac{{\cos {\theta _1}}}{{{\rho _1}}} = \frac{{\cos {\theta _2}}}{{{\rho _2}}} = \frac{{\cos {\theta _3}}}{{{\rho _3}}}$$
$$\eqalign{ & {\text{Thus,}}\,\cos \theta \propto \rho \cr & \therefore {\rho _1} > {\rho _2} > {\rho _3} \cr & \therefore \cos {\theta _1} > \cos {\theta _2} > \cos {\theta _3} \cr & 0 \leqslant {\theta _1} < {\theta _2} < {\theta _3} < \frac{\pi }{2} \cr} $$