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The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r1, while water rises by the same amount in a capillary tube of radius r2. The ratio (r1/r2) is then close to:
- 2/3
- 4/5
- 2/5
- 3/5
Correct answer: 2/5
Solution
The ratio of the radii of the capillary tubes can be derived from the relationship between surface tension, density, and contact angle in capillary action. Given that mercury has a much higher surface tension and a larger contact angle compared to water, the ratio of the radii (r1/r2) is influenced by these factors, leading to the conclusion that it is approximately 2/5.
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