If a capillary tube of radius $1 \,mm$ is immersed in water, the mass of water rising in the capillary tube is $m$. If the radius of the capillary tube is doubled, then the mass of water that rises in the same capillary tube will be

$A$ glass capillary of radius $0.35 \ mm$ is inclined at $60^{\circ}$ with the vertical in water. The length of the water column in the capillary is (surface tension of water $= 7 \times 10^{-2} \ N/m$,acceleration due to gravity $g = 10 \ m/s^2$,$\cos 0^{\circ} = 1$,$\cos 60^{\circ} = 0.5$,density of water $\rho = 10^3 \ kg/m^3$) (in $cm$)

The sap in trees,which consists mainly of water in summer,rises in a system of capillaries of radius $r = 2.5 \times 10^{-5} \ m$. The surface tension of sap is $T = 7.28 \times 10^{-2} \ N/m$ and the angle of contact is $0^{\circ}$. Does surface tension alone account for the supply of water to the top of all trees?

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

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 $\,cm$)

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