If a capillary tube is immersed in water, rise of water in capillary is h 1 . When the whole arrangement is taken to a depth d in a mine, the water level rises to h 2 . The ratio h 1 h 2 is

Question

If a capillary tube is immersed in water, rise of water in capillary is h 1 ​ . When the whole arrangement is taken to a depth d in a mine, the water level rises to h 2 ​ . The ratio h 1 ​ h 2 ​ ​ is (R=radius of earth)

TestHub · Accepted Answer

The height of capillary rise is given by $h = \frac{2 T cos θ}{ρ g r}$

This implies $h \propto \frac{1}{g}$

At the surface of the earth, acceleration due to gravity is $g_{1} = g$

At a depth $d$ in a mine, acceleration due to gravity is $g_{2} = g (1 - \frac{d}{R}) = g (\frac{R - d}{R})$

The ratio of capillary rise is $\frac{h _{2}}{h _{1}} = \frac{g _{1}}{g _{2}}$

Substituting the values, we get $\frac{h _{2}}{h _{1}} = \frac{g}{g ( \frac{R - d}{R} )} = \frac{R}{R - d}$

Answer: $\frac{R}{( R - d )}$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion