$A$ liquid (density $= 10^3 \ kg/m^3$) rises to a height of $10 \ cm$ in a capillary tube. If the angle of contact of the liquid-glass pair is $0^{\circ}$ and the radius of the tube is $2 \ mm$,then the surface tension of the liquid is:

$A$ capillary tube is immersed vertically in water and the height of the water column is $x$. When this arrangement is taken into a mine of depth $d$,the height of the water column is $y$. If $R$ is the radius of earth,the ratio $\frac{x}{y}$ is

Given below are two statements:
$Statement$ $I$: If a capillary tube is immersed first in cold water and then in hot water,the height of capillary rise will be smaller in hot water.
$Statement$ $II$: If a capillary tube is immersed first in cold water and then in hot water,the height of capillary rise will be smaller in cold water.
In the light of the above statements,choose the most appropriate from the options given below:

In a capillary tube of area of cross-section '$a$',water rises to a height '$h$'. To what height will water rise in a capillary tube of area of cross-section $4a$?

Water rises to a height $3$ cm in a capillary tube. If the cross-sectional area of the capillary tube is reduced to $1/3^{rd}$ of its initial area, then water will rise to a height of:

The surface tension for pure water in a capillary tube experiment is