Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are $0.8$ and $0.6$ and surface tensions are $60$ and $50 \text{ dyne/cm}$ respectively. The ratio of the heights of the liquids in the two tubes $\frac{h_1}{h_2}$ is:

Water rises to a height of $10 \,cm$ in a capillary tube. In which of the following conditions will it rise to a height much greater than $10 \,cm$ in a very long capillary tube?

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 to a height of $20 \,mm$ in a capillary tube of cross-sectional area $A$. If the area of cross-section of the tube is made $\frac{A}{4}$, then water will rise to a height of (in $\,cm$)

$A$ 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 $\theta$.

If two glass plates are placed very close to each other in water,then there will be a force of: