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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 water in the capillary tube is <img alt="5 \mathrm{~g}" src="https://entrancecorner.oncodecog

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

Option: 1

2.5 g


Option: 2

5.0 g


Option: 3

10 g


Option: 4

20 g


Answers (1)

best_answer

Mass of water in first tube is

                    \mathrm{ m=\pi r^2 h \rho }
Now, surface tension \mathrm{\sigma=\frac{h \rho g r}{2}=\frac{h^{\prime} \rho g r^{\prime}}{2}} where \mathrm{h^{\prime}} is the height to which water rises in the second tube and \mathrm{r^{\prime}} its radius.

Since \mathrm{r^{\prime}=2 r, h^{\prime}=h / 2}. Therefore, the mass of water in the second capillary tube is
\mathrm{ \begin{aligned} m^{\prime} & =\pi r^{\prime 2} h^{\prime} \rho=\pi(2 r)^2 \frac{h}{2} \rho \\ & =2 \pi r^2 h \rho=2 m=2 \times 5=10 \mathrm{~g} \end{aligned} }

Posted by

Deependra Verma

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