Answer :
The formula for the height of liquid rise in a capillary tube is inversely proportional to the radius of the tube, showing that a smaller radius will result in a higher liquid rise due to the reduced liquid mass in the tube needed to balance the force of surface tension.
The rise of liquid in a capillary tube is a classic example of the influence of surface tension on liquid behavior. When a capillary tube is placed in a liquid, the liquid will rise or fall inside the tube depending on the interaction between the tube's material and the liquid. The height to which the liquid rises (h) can be expressed in terms of the surface tension of the liquid (), the density of the liquid (p), the gravitational acceleration (g), and the radius of the capillary tube (r). The formula that encapsulates this relationship is h = (2 cos )/(rgp), where is the contact angle between the liquid and the tube. This relationship indicates that the height is directly proportional to the surface tension and inversely proportional to the radius of the tube and the density of the liquid.
To demonstrate that the height is inversely proportional to the radius, we look at the formula and see that h and r are inversely related; that is, as the radius (r) decreases, the height (h) increases. This is because, for smaller tubes, less liquid mass is needed to balance the upward force created by surface tension. Hence, a smaller radius results in a higher rise of the liquid. For example, if the radius of the tube is halved, all other factors being constant, the height of the liquid rise will double.
