Water rises to a height h in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be

The correct option is 6h.

Let us analyze the physics of capillary rise step-by-step.
The height $h$ to which a liquid rises in a capillary tube of radius $r$ is given by Ascent's formula:
$h=\frac{2T\cos \theta }{r\rho g}$
where:
- $T$ is the surface tension of the liquid,
- $\theta$ 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.

For the same liquid (water) and the same capillary tube, the parameters $T$, $\theta$, $r$, and $\rho$ remain constant.
Therefore, the height $h$ is inversely proportional to the acceleration due to gravity $g$:
$h\propto \frac{1}{g}$

Let $g_e$ be the acceleration due to gravity on the surface of the Earth, and $g_m$ be the acceleration due to gravity on the surface of the Moon.
We know that the gravity on the Moon is one-sixth of the gravity on the Earth:
$g_m=\frac{g_e}{6}$

Let $h_e=h$ be the height of the water column on Earth, and $h_m$ be the height on the Moon.
Using the inverse relationship:
$\frac{h_m}{h_e}=\frac{g_e}{g_m}$
Substitute $g_m=\frac{g_e}{6}$ into the equation:
$\frac{h_m}{h}=\frac{g_e}{\left(\frac{g_e}{6}\right)}=6$
Multiplying both sides by $h$ gives:
$h_m=6h$

Thus, the height of the water column in the same capillary tube on the surface of the Moon will be 6h.