Water rises to a height of $10 \ cm$ in a certain capillary tube. Another identical tube when dipped in mercury,the level of mercury is depressed by $3.42 \ cm$. The density of mercury is $13.6 \ g/cc$. The angle of contact for water in contact with glass is $0^o$ and for mercury in contact with glass is $135^o$. The ratio of the surface tension of water to that of $Hg$ is:

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 $3 \,cm$ 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 $\,cm$)

Liquid rises to a height $2 \ cm$ in a capillary tube; in that case,the angle of contact between the solid and the liquid is $0^{\circ}$. The tube is lowered more now,so that the capillary is only $1 \ cm$ above the liquid. In this case,the angle of contact between the solid and liquid is $......^{\circ}$.

The angle of contact between glass and water is $0^\circ$ and it rises in a capillary up to $6 \text{ cm}$ when its surface tension is $70 \text{ dynes/cm}$. Another liquid of surface tension $140 \text{ dynes/cm}$,angle of contact $60^\circ$ and relative density $2$ will rise in the same capillary by ........ $\text{cm}$.

Two capillary tubes $P$ and $Q$ are dipped vertically in water. The height of water level in capillary tube $P$ is $\frac{2}{3}$ of the height in capillary tube $Q$. The ratio of their diameters is