Water rises to a height of $10 \, cm$ in a capillary tube and mercury falls to a depth of $3.1 \, cm$ in the same capillary tube. If the density of mercury is $13.6 \, g/cm^3$ and the angle of contact for mercury is $135^{\circ}$,the approximate ratio of surface tensions of water and mercury is

$A$ $U$-tube is such that the diameter of one limb is $0.4\,mm$ and that of the other is $d\,mm$. If the surface tension of water contained in the tube is $0.07\,N/m$ and the difference in the levels of liquid in the limbs is $3.6\,cm$,then the value of $d$ is:

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 $......^{\circ}$.

$A$ narrow glass capillary tube of radius $1.00 \ mm$ is dipped in a trough containing mercury. The amount by which the level of mercury dips down relative to the normal level outside the tube will be approximately $..... \ mm$.
$[$Surface tension of mercury at room temperature $= 0.465 \ N/m$,density of mercury $= 13.6 \times 10^3 \ kg/m^3$,angle of contact with glass $= 135^{\circ}$,$g = 9.8 \ m/s^2]$

$A$ glass capillary tube of inner diameter $0.28 \,mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel is ............ $\times 10^3 \,N/m^2$ (surface tension of water $= 0.07 \,N/m$ and atmospheric pressure $= 10^5 \,N/m^2$).

$A$ capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of the water in the capillary is $5 \, g$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is $........ \, g$.