Question:
In a capillary tube, water rises to \(3\ \text{mm}\). The height of water that will rise in another capillary tube having one-third radius of the first is
In a capillary tube, water rises to \(3\ \text{mm}\). The height of water that will rise in another capillary tube having one-third radius of the first is
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\(h = \frac{2T\cos\theta}{\rho g r}\). Narrower tube gives greater rise.
Updated On: Apr 23, 2026
- \(1\ \text{mm}\)
- \(3\ \text{mm}\)
- \(6\ \text{mm}\)
- \(9\ \text{mm}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Capillary rise \(h \propto \frac{1}{r}\). So \(h_1 r_1 = h_2 r_2\).
Step 2: Detailed Explanation:
Given \(h_1 = 3\ \text{mm}\), \(r_2 = r_1/3\).
\(h_2 = \frac{h_1 r_1}{r_2} = \frac{3 \times r_1}{r_1/3} = 3 \times 3 = 9\ \text{mm}\).
Step 3: Final Answer:
Thus, height = \(9\ \text{mm}\).
Capillary rise \(h \propto \frac{1}{r}\). So \(h_1 r_1 = h_2 r_2\).
Step 2: Detailed Explanation:
Given \(h_1 = 3\ \text{mm}\), \(r_2 = r_1/3\).
\(h_2 = \frac{h_1 r_1}{r_2} = \frac{3 \times r_1}{r_1/3} = 3 \times 3 = 9\ \text{mm}\).
Step 3: Final Answer:
Thus, height = \(9\ \text{mm}\).
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