Rankers Physics

Surface Tension and Viscosity: Practice Problem & Solution

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 $5\text{ g}$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is: (2020)
$5.0\text{ g}$
$10.0\text{ g}$
$20.0\text{ g}$
$2.5\text{ g}$

Solution Explained:

To solve this problem, we apply the core principles of Surface Tension and Viscosity. Understanding the underlying formula is key to arriving at the correct answer below:

Mass of water risen in capillary $m = \pi r^2 h \rho$. Since $h \propto \frac{1}{r}$, we get $m \propto r$. Thus, $m_2 = m_1 \left(\frac{r_2}{r_1}\right) = 5 \times \left(\frac{2r}{r}\right) = 10\text{ g}$.

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