Calculate the ratio of the heights to which water and mercury are raised by capillary action in the same glass tube.

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

The Cohesive forces are attractive forces between molecules of the same sort. Adhesive forces are the attractive forces that exist between molecules of various sorts. The surface of a liquid contracts to the lowest feasible surface area due to cohesive forces between molecules. This overall impact is referred to as surface tension is a term used to describe the force that exists.

The capillary action is the propensity of a fluid to rise or fall in a narrow tube, or capillary tube, according to the relative strength of the capillary’s adhesiveness and cohesion.

\[h = \frac{{2\sigma \cos \theta }}{{\rho gr}}\]

The angle of contact between glass and mercury is \[{\rm{140}}\] degrees.

The angle of contact between glass and water is \[{\rm{0}}\] degree.

By putting all the value into the equation, we get:

Here,\[{\rho _w}\]is the density of water,\[{\rho _m}\]is the density of mercury,\[{\sigma _w}\]is the surface tension of water, and\[{\sigma _w}\]is the surface tension of the mercury.

Calculating further,

\[\begin{array}{c}\frac{{{h_w}}}{{{h_m}}} = \frac{{{\sigma _w}\cos {\theta _w}}}{{{\sigma _m}\cos {\theta _m}}} \times \frac{{{\rho _m}}}{{{\rho _w}}}\\\frac{{{h_w}}}{{{h_m}}} = \frac{{\left( {0.0728} \right)\cos \left( {0^\circ } \right)}}{{\left( {0.465} \right)\cos \left( {140^\circ } \right)}} \times \frac{{13600}}{{1000}}\\\frac{{{h_w}}}{{{h_m}}} = \frac{{2.78}}{{ - 1}}\end{array}\]

Therefore, water rises up to 2.78 units of length from the surface of water level in the basin, level to the mercury which falls one unit.