Upon dipping a capillary tube into a liquid, the liquid level...

The height of the liquid column in a capillary tube is given by Jurin's law:

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

where $T$ is the surface tension, $\theta$ is the angle of contact, $\rho$ is the density of the liquid, $g$ is the acceleration due to gravity, and $r$ is the radius of the capillary tube.

Given that the liquid level neither rises nor falls, $h = 0$.

$\dfrac{2T \cos \theta}{\rho g r} = 0$

Since $\rho$, $g$, and $r$ are non-zero constants for a given setup, we must have:

$T \cos \theta = 0$

This implies that either $T = 0$ or $\cos \theta = 0$.

If $\cos \theta = 0$, then the angle of contact \theta = 90^{}^{{}^{\circ}}.

If $T = 0$, then the surface tension of the liquid is zero.

Thus, the angle of contact may be 90^{}^{{}^{\circ}} or the surface tension may be zero.