What is capillary action? Derive the formula for rise of liquid in a capillary tube immersed vertically in liquid.

Hint: To define capillarity or capillary action we have to first know what capillarity is. The phenomenon of the rise and fall of a liquid in a capillary tube is called capillary action or capillarity. We can define a capillary tube as a fine tube. When we immerse a liquid in water, the water will rise in the tube.

Complete answer:
When a capillary tube is dipped in a liquid, the liquid level either rises or falls in the capillary tube. The phenomenon of rise or fall of a liquid level in a capillary tube is called capillary or capillary action.
When a liquid rises in a capillary tube, the weight of the column of the liquid of density $\rho $ inside the tube is supported by the upward force of surface tension acting around the circumference of the point of contact.
$\pi {{r}^{2}}\left( h+\dfrac{r}{3} \right)\rho g=T\cos \theta \times 2\pi r$
Then surface tension,
$T=\dfrac{r(h+\dfrac{r}{3})\rho g}{2\cos \theta }$
Where, h is the height of the liquid column above the liquid meniscus.
$\rho $ is the density of the liquid
‘r’ is the inner radius of the capillary tube
$\theta $ is the angle of contact.

Note: Surface tension is the property of a liquid by virtue of which its free surface at rest behaves as an elastic skin or a stretched rubber membrane with a tendency to contract so as to contract as to occupy minimum surface area. The phenomenon of surface tension has been well explained by the molecular theory of matter.