$A$ capillary tube is taken from the Earth's surface to the Moon's surface. What happens to the rise of the liquid column on the Moon's surface? (Acceleration due to gravity on the Earth's surface is six times that of the Moon's surface.)

Two narrow bores of diameters $3.0 \;mm$ and $6.0 \;mm$ are joined together to form a $U$-tube open at both ends. If the $U$-tube contains water,what is the difference (in $mm$) in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is $7.3 \times 10^{-2} \;N m^{-1}$. Take the angle of contact to be zero and density of water to be $1.0 \times 10^{3} \;kg m^{-3}$ $(g = 9.8 \;m s^{-2})$.

When a capillary tube is immersed in water vertically,water rises to a height $h$ inside the tube. If the radius of another capillary tube is $\frac{1}{3}$ that of the previous,the height to which water will rise in this tube 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:

Water rises in a capillary tube to a height such that the upward force of surface tension balances the downward force of $75 \times 10^{-4} \ N$ due to the weight of the water. If the surface tension of water is $12 \times 10^{-2} \ N/m$,the internal circumference of the capillary must be:

Water rises to a height of $16.3 \, cm$ in a capillary tube of height $18 \, cm$ above the water level. If the tube is cut at a height of $12 \, cm$ above the water level,then: