Question

A long capillary tube of radius of $0.2mm$ is placed vertically inside a beaker of water. If the tube is now pushed into water so that only $5.0cm$ of its length is above the surface, then determine the angle of contact between the liquid and glass surface.

• A. ${\cos }^{-1}\left(\frac{4}{5}\right)$
• B. ${\cos }^{-1}\left(\frac{5}{7}\right)$
• C. ${\cos }^{-1}\left(\frac{3}{5}\right)$
• D. ${\cos }^{-1}\left(\frac{5}{4}\right)$

Answer 1

The correct option is B ${\cos }^{-1}\left(\frac{5}{7}\right)$

Surface tension of water be $70\times {10}^{-3}\frac{N}{m}$

$h=\frac{2T\cos \theta }{rg\rho }$

$\cos \theta$$=\frac{\rho ghr}{2T}$

$=\frac{{10}^3\left(10\right)(5\times {10}^{-2})(0.2\times {10}^{-3})}{2(70\times {10}^{-3})}$

$=\frac{5}{7}$