A capillary tube of radius is immersed in water and water rises in it to a height . The mass of the water in the capillary is 5 g. Another capillary tube of radius is immersed in water. The mass of water that will rise in this tube is [2020

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Solution

Q.
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 $2 r$ is immersed in water. The mass of water that will rise in this tube is [2020]

1 2.5 g

2 5.0 g

3 10.0 g

4 20.0 g

Ans.
(3)

Force of surface tension balances the weight of water in capillary tube.

$F_{s} = T \cos θ (2 π r) = m g$

$m \propto r$

Hence, $\frac{m'}{m} = \frac{r'}{r} \Rightarrow \frac{m'}{5 g} = \frac{2 r}{r} \Rightarrow m' = 10$ $g$

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