Question

A vertical capillary with inside diameter 0.50 mm is submerged into water so that the length of its part emerging outside the water surface is equal to 25 mm. Find the radius of curvature of the meniscus. Surface tension of water is $73\times {10}^{-3}$ N/m.

Answer 1

In the capillary tube, the water should rise to a height

$H=\frac{2T}{r\rho g}$

Here $T=73\times {10}^{-3}Nm,r=\frac{0.50mm}{2}=0.25\times {10}^{-3}m$

$\rho ={10}^{3}kg/m^3$

$\therefore h=\frac{2\times 73\times {10}^{-3}}{0.25\times {10}^{-3}\times {10}^3\times 9.8}=59\times {10}^{-3}m=59mm$

Now h > r. i.e., length is outside water surface. Therefore, radius of meniscus> radius of capillary r.If R is the radius of meniscus. then we have $\frac{2T}{R}=h\rho g$

$orR=\frac{2T}{h\rho g}$

$Hereh=25mm=25\times {10}^{-3}m$

$R=\frac{2\times 73\times {10}^{-3}}{25\times {10}^{-3}\times {10}^3\times 9.8}=0.6\times {10}^{-3}=0.6mm$