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 ....... $dyne/cm$.

Three liquids have the same surface tension and have densities $\rho_1, \rho_2$, and $\rho_3$ $(\rho_1 > \rho_2 > \rho_3)$. In three identical capillaries, the rise of liquid is the same. The corresponding angles of contact $\theta_1, \theta_2$, and $\theta_3$ are related as:

In a $U$-shaped tube,the radius of one limb is $2 \ mm$ and that of the other limb is $4 \ mm$. $A$ liquid of surface tension $0.03 \ Nm^{-1}$,density $1500 \ kgm^{-3}$,and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $mm$)

Radius of a capillary is $2 \times 10^{-3} \,m$. $A$ liquid of weight $6.2 \times 10^{-4} \,N$ may remain in the capillary. Then the surface tension of the liquid will be $:-$

In a capillary tube of radius '$R$',a straight thin metal wire of radius '$r$' is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the capillary and the thin wire are at the same level. If '$T$' is the surface tension of water and '$\rho$' is the density of water, then the rise of water in the capillary is:

Why does the mercury level fall in a capillary tube? Explain.