The correct relation for the capillary rise $h$ in a tube of radius $r$ is:

The kerosene oil rises up in the wick of a lamp ...........

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:

When one end of a capillary tube is dipped in water,the height of water column is $h$. The upward force of $105 \text{ dyne}$ due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is (Surface tension of water $= 7 \times 10^{-2} \text{ N/m}$) (in $\text{ cm}$)

Water rises to a height of $3 \,cm$ in a capillary tube. If the cross-sectional area of the capillary tube is reduced to $1/9$th of its initial area, then the water will rise to a height of: (in $\,cm$)

Water rises to a height of $2 \,cm$ in a capillary tube. If the cross-sectional area of the tube is reduced to $\frac{1}{16}^{\text{th}}$ of the initial area, then water will rise to a height of: (in $\,cm$)