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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 \(5 \mathrm{~g}\). Another capillary tube of radius \(2 r\) is immersed in water. The mass of water that will rise in this tube is
(a) \(2.5 \mathrm{~g}\)
(b) \(5.0 \mathrm{~g}\)
(c) \(10 \mathrm{~g}\)
(d) \(20 \mathrm{~g}\)

3 Answers

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Correct option (c) \(10 \mathrm{~g}\)
Explanation:
$$
h=\frac{2 S \cos \theta}{r \rho g}
$$
Mass of water in the first tube,
$$
\begin{aligned}
m &=\pi r^{2} h \rho=\pi r^{2} \times\left(\frac{2 S \cos \theta}{r \rho g}\right) \times \rho \\
&=\frac{2 \pi r S \cos \theta}{g}
\end{aligned}
$$
$$
\begin{array}{ll}
\therefore \quad m \propto r . \text { Hence, } \frac{m^{\prime}}{m}=\frac{2 r}{r}=2 \\
\text { or } \quad m^{\prime}=2 m=2 \times 5 g=10 g .
\end{array}
$$
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