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Answer :
Final answer:
The height of water that will rise in the second capillary tube with one-third the radius of the first will be 3 mm.
Explanation:
In order to find the height of water that will rise in another capillary tube with one-third the radius of the first, we can use the radius-height relationship for capillary action. This relationship states that the height to which a fluid rises in a capillary tube is inversely proportional to the radius of the tube.
Let's assume that the height of water in the first capillary tube is h. Since the radius of the second tube is one-third of the first, the radius of the second tube is (1/3) * 3 mm = 1 mm. Using the radius-height relationship, we can set up the following proportion: (h / 3 mm) = (1 mm / 1 mm). Cross-multiplying and solving for h, we find that the height of water in the second capillary tube will be h = 3 mm / 1 mm = 3 mm.
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