Physics - Fluid Question with Solution | TestHub

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

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

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

Since $T$, $\theta$, $r$, and $\rho$ remain constant, the capillary rise is inversely proportional to the acceleration due to gravity:

$h\propto \frac{1}{g}$

Given that the acceleration due to gravity on the earth is $6$ times that on the moon, we have $g_e=6g_m$.

Therefore, the ratio of the capillary rise on the moon to that on the earth is:

$\frac{h_m}{h_e}=\frac{g_e}{g_m}=\frac{6g_m}{g_m}=6$

$h_m=6h_e$

The rise of the liquid column on the moon is $6$ times that on the earth's surface.

Answer: $6$ times that of earth's surface