Answer :
Halving the diameter of the capillary tube results in the water level rising to double the original height due to the inverse relationship between the capillary rise and the radius of the tube, which is a fundamental concept of capillarity.
When water rises to a height h in a capillary tube of a certain diameter, the height of the water column is inversely proportional to the radius of the tube. This relationship is described by the equation h = (2T cos \\theta)/(rpg), where T is the surface tension of the water, \\theta is the contact angle, r is the radius of the tube, p is the density of the water, and g is the acceleration due to gravity.
If the diameter of the capillary tube is halved, that means the radius is also halved. According to the formula, since the radius (r) appears in the denominator, halving the radius would result in the water level rising to double the height, assuming other conditions remain constant. This is due to the phenomenon of capillarity or capillary action, where the adhesion between water molecules and the glass surface causes water to rise in the glass tube.
