In a capillary tube,water rises by $1.2 \ mm$. The height of water that will rise in another capillary tube having half the radius of the first is ........ $mm$.

When a long glass capillary tube of radius $0.015 \; cm$ is dipped in a liquid,the liquid rises to a height of $15 \; cm$ within it. If the contact angle between the liquid and glass is close to $0^{\circ}$,the surface tension of the liquid,in $milliNewton \; m^{-1}$ is $.....$
$[\rho_{\text{liquid}} = 900 \; kg \; m^{-3}, g = 10 \; ms^{-2}]$ (Give answer in closest integer)

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

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).

This question has Statement-$I$ and Statement-$II$. Of the four choices given after the statements,choose the one that best describes the two statements.
Statement-$I$: $A$ capillary is dipped in a liquid and liquid rises to a height $h$ in it. As the temperature of the liquid is raised,the height $h$ increases (if the density of the liquid and the angle of contact remain the same).
Statement-$II$: Surface tension of a liquid decreases with the rise in its temperature.

$A$ 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).