Water rises in a capillary tube to a height of $3\, cm$ when one end is dipped vertically in it. If the surface tension of water is $75 \times 10^{-3}\, N/m$,then the diameter of the capillary tube will be....... $mm$. (Assume $g = 10\, m/s^2$)

When a capillary is dipped in water,water rises to a height $h$. If the length of the capillary is made less than $h$,then

$A$ glass capillary tube is in the shape of a truncated cone with an apex angle $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically,water rises in it to a height $h$,where the radius of its cross section is $b$. If the surface tension of water is $S$,its density is $\rho$,and its contact angle with glass is $\theta$,the value of $h$ will be ($g$ is the acceleration due to gravity).

Two long capillary tubes $A$ and $B$ of radius $R_B > R_A$ are dipped in the same liquid. Then:

$A$ 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).

$A$ glass rod of radius $1.0\,mm$ is inserted symmetrically into a vertical capillary tube of radius $2.0\,mm$ such that their lower ends are at the same level. This arrangement is now dipped in water. The height to which water will rise into the tube will be ...... $mm$ (Surface Tension of water $T = 75 \times 10^{-3}\,N/m$,density $\rho = 10^3\,kg/m^3$,$g = 10\,m/s^2$).