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 $\,cm$)

When a capillary tube is dipped into two liquids having relative densities $0.8$ and $0.6$ and surface tensions $60 \, dyne/cm$ and $50 \, dyne/cm$ respectively,the ratio of the heights of the liquids in the capillary tube $\frac{h_1}{h_2}$ is:

Two tubes of same length and diameters $4 \ mm$ and $8 \ mm$ are joined together to form a $U$-shaped tube open at both the ends. If the $U$-tube contains water,then the difference between the levels of water in the two limbs of the tube is (Surface tension of water at the temperature of experiment is $7.3 \times 10^{-2} \ N \ m^{-1}$,angle of contact $= 0^{\circ}$,density of water $= 1.0 \times 10^3 \ kg \ m^{-3}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $mm$)

$A$ 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:

In the state of weightlessness,a capillary tube is dipped in water,then water

Given below are two statements:
Statement $I$: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement $II$: The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
In the light of the above statements,choose the correct answer from the options given below: