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  • When a capillary tube of radius r is immersed in a liquid of density , the liquid rises to a height h in it.

When a capillary tube of radius r is immersed in a liquid of density \rho, the liquid rises to a height h in it. If m is the mass of the liquid in the capillary tube, the potential energy of this mass of the liquid in the tube is

Option: 1

m g h / 4


Option: 2

m g h / 2


Option: 3

m g h


Option: 4

2 m g h


Answers (1)

best_answer

The mass of the liquid in a column between x and \mathrm{ x+d x} is

\mathrm{ d m=\pi r^2 \rho d x }
Therefore, the potential energy of the liquid in a column of height h is
\mathrm{ \begin{aligned} & \int_0^h\left(\pi r^2\right) x \rho g d x=\pi r^2 \rho g \int_0^h x d x \\\\ & =\pi r^2 \rho g \frac{h^2}{2}=\left(\pi r^2 h \rho\right) g h / 2 \\\\ & =m g h / 2 \\ & \end{aligned} }

Posted by

Deependra Verma

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