Question

The nature of $r - h$ graph ($'r'$ is the radius of capillary tube and $'h'$is the capillary rise) is:
A) Straight line
B) Parabola
C) Ellipse
D) Rectangular hyperbola

Answer 1

In the capillary tube method, we immerse a capillary tube of radius $r$ vertically in a liquid to a depth ${h_1}$. The liquid under the experiment will have a density $\rho$. The meniscus will be forced down to the lower end of the capillary and is held there by pressure. The capillary rise is proportional to the surface tension and inversely proportional to the radius of the capillary tube and the acceleration due to gravity.

Complete step by step solution:
The rise of a liquid through a narrow tube against gravity without the help of any external force is called capillary rise. Capillary action happens when the adhesion between the molecules of the liquid and the walls of the tube will be greater than the cohesive force between the molecules of the liquid.
The rise of the liquid through a capillary tube will be directly proportional to the surface tension of the liquid and it will be inversely proportional to the radius of the capillary tube and the acceleration due to gravity.
The height of capillary rise is given by,
$h = \dfrac{{2S}}{{\rho rg}}$
where $S$ is the surface tension, $\rho$ is the radius of the fluid, $r$ is the radius of the capillary tube and $g$ is the acceleration due to gravity.
From the equation of height, we can see that height is inversely proportional to the radius, i.e.
$h \propto \dfrac{1}{r}$
Therefore the nature of the $r - h$ curve will be a rectangular parabola

The answer is option (D) Rectangular hyperbola.

Note: The capillary rise will decrease with the increase in the radius of the capillary tube. Capillary action has a significant role in our day to day life. The rise of oil through the wick of a lamp is due to capillary action. Capillary action takes place in fountain pens. The forces behind the capillary rise are adhesion, cohesion, and surface tension.