Water rises to a height $h$ in a capillary tube at the surface of the Earth. On the surface of the moon,the height of the water column in the same capillary tube will be:

The following observations were taken for determining surface tension $T$ of water by the capillary method:
Diameter of capillary,$D = 1.25 \times 10^{-2} \; m$
Rise of water,$h = 1.45 \times 10^{-2} \; m$
Using $g = 9.80 \; m/s^2$ and the simplified relation $T = \frac{rhg}{2} \times 10^3 \; N/m$,the possible error in surface tension is ........... $\%$. (Assume the least count of the measuring instrument is $0.01 \times 10^{-2} \; m$)

$A$ glass rod of radius $r_1$ is inserted symmetrically into a vertical capillary tube of radius $r_2$ $(r_1 < r_2)$ such that their lower ends are at the same level. The arrangement is dipped in water. The height to which water will rise into the tube will be ($\rho =$ density of water,$T =$ surface tension of water,$g =$ acceleration due to gravity).

Three liquids have the same surface tension and densities $\varrho_{1}, \varrho_{2}$,and $\varrho_{3}$ $(\varrho_{1} > \varrho_{2} > \varrho_{3})$. In three identical capillaries,the rise of liquid is the same. The corresponding angles of contact $\theta_{1}, \theta_{2}$,and $\theta_{3}$ are related as:

Liquid rises to a height $2 \ cm$ in a capillary tube; in that case,the angle of contact between the solid and the liquid is $0^{\circ}$. The tube is lowered more now,so that the capillary is only $1 \ cm$ above the liquid. In this case,the angle of contact between the solid and liquid is $......^{\circ}$.

The water rises in the capillary to a height of $10\, cm$. If the surface tension of water is $73 \times 10^{-3}\, N/m$,density is $10^3\, kg/m^3$ and $g = 9.8\, m/s^2$,then find the radius of the capillary. (in $, cm$)