Question

A glass capillary tube of internal radius $r=0.25mm$ is immersed in water. The top end of the tube projected by $2cm$ above the surface of the water. At what angle does the liquid meet the tube? Surface tension of water $=0.7N/m$.

• A. $\theta ={90}^{\circ }$
• B. $\theta ={70}^{\circ }$
• C. $\theta ={45}^{\circ }$
• D. $\theta ={35}^{\circ }$

Answer 1

The correct option is B $\theta ={70}^{\circ }$

Water wets glass and so the angle of contact is zero.
For full rise, neglecting the small mass in the meniscus.
$2\pi rT=\pi r^{2}h\rho g\Rightarrow h=\frac{2T}{r\rho g}[\because$ water wets glass, $\theta =0^{\circ }]$
$=\frac{2\times 0.07}{0.25\times {10}^{-3}\times 1000\times 9.8}$
As the tube is only $2cm$ above the water and so, water will rise by $2cm$ and meet the tube at an angle such that,
$2\pi rT\cos \theta =\pi r^2{h}^{\prime }\rho g$
$\Rightarrow 2T\cos \theta =h^{\prime }r\rho g$
$\Rightarrow \cos \theta =\frac{h^{\prime }r\rho g}{2T}$
$=\frac{2\times {10}^{-2}\times 0.25\times {10}^{-3}\times 1000\times 9.8}{2\times 0.07}$
The liquid will meet the tube at an angle, $\theta \cong {70}^{\circ }$.