Answer :
Final answer:
The height of water that will rise in the second capillary tube, which has one-third the radius of the first tube, will be nine times the height in the first tube. So the correct option is D .
Explanation:
When water rises in a capillary tube, it does so due to a phenomenon called capillary action. Capillary action is the result of the cohesive forces within a liquid and the adhesive forces between the liquid and the walls of the tube. The height to which water rises in a capillary tube is inversely proportional to the radius of the tube. This means that if the radius of the first capillary tube is one-third that of the second capillary tube, the height of water that will rise in the second tube will be three times the height in the first tube.
Let's say the height of water in the first capillary tube is 3mm. Since the second capillary tube has one-third the radius, its radius would be three times smaller than the first tube. Let's represent the radius of the first tube as R, and the radius of the second tube as r. We know that the height of water is inversely proportional to the radius. So, we can set up the equation as:
Height of second tube = (3mm * 3R) / r = (9mmR) / r
This means that the height of water in the second capillary tube is 9mm.
