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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:

1. 5.0 g
2. 10.0 g
3. 20.0 g
4. 2.5 g

Correct answer: 10.0 g

Solution

The height of water in a capillary is inversely proportional to the radius of the tube (h ∝ 1/r). The volume of water in the capillary is proportional to the product of the height and the square of the radius (V ∝ h × r²). Doubling the radius (2r) reduces the height to h/2, but the cross-sectional area increases by a factor of 4. Thus, the mass of water (proportional to volume) becomes 2 × 5 g = 10 g.

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