$A$ capillary tube $(A)$ is dipped in water. Another identical tube $(B)$ is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

$A$ uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
$(A)$ For a given material of the capillary tube,$h$ decreases with increase in $r$.
$(B)$ For a given material of the capillary tube,$h$ is independent of $\sigma$.
$(C)$ If this experiment is performed in a lift going up with a constant acceleration,then $h$ decreases.
$(D)$ $h$ is proportional to contact angle $\theta$.

The radius of the bore of a capillary tube is $r$ and the angle of contact of the liquid is $\theta$. When the tube is dipped in the liquid,the radius of curvature of the meniscus of liquid rising in the tube is

$A$ 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).

Water rises up to a height $h$ in a capillary tube immersed vertically in water. When this whole arrangement is taken to a depth $d$ in a mine,the water level rises up to a height $h^{\prime}$. If $R$ is the radius of the earth,then the ratio $\frac{h}{h^{\prime}}$ is

Fill in the blanks:
$(i)$ Smaller the radius of the capillary tube,...... the height of the column. ( more / less )
$(ii)$ If the meniscus is convex,then the liquid .......... in the capillary,and if it is concave,then the liquid .......... in the capillary. ( depressed / rises up )