In a vessel, equal masses of alcohol (specific gravity $0.8$) and water are mixed together. A capillary tube of radius $1 \, mm$ is dipped vertically in it. If the mixture rises to a height of $5 \, cm$ in the capillary tube, the surface tension of the mixture is ....... $dyne/cm$.

$A$ capillary tube is taken from the Earth's surface to the Moon's surface. What happens to the rise of the liquid column on the Moon's surface? (Acceleration due to gravity on the Earth's surface is six times that of the Moon's surface.)

Two narrow tubes of diameters $d_1$ and $d_2$ are joined together to form a $U$-tube open at both ends. If the $U$-tube contains water,the difference in water levels in the limbs is ($T$ is the surface tension of water,the angle of contact is zero,the density of water is $\rho$,and $g$ is the acceleration due to gravity).

$A$ capillary tube is vertically immersed in water,and water rises up to a height $h_{1}$. When the whole arrangement is taken to a depth $d$ in a mine,the water level rises up to a height $h_{2}$. The ratio $h_{1} / h_{2}$ is ($R =$ radius of earth).

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:

The height up to which water will rise in a capillary tube will be