Question

A glass capillary tube is of truncated cone with an apex angle of $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height $h$, where the radius of its cross section is $b$. If the surface tension of water is $S$, its density is $\rho$, and its contact angle with glass is $\theta$, the value of $h$ will be ($g$ is the acceleration due to gravity)

• A. $\frac{2S}{b\rho g}\cos (\theta -\alpha )$
• B. $\frac{2S}{b\rho g}\cos (\theta +\alpha )$
• C. $\frac{2S}{b\rho g}\cos (\theta -\alpha /2)$
• D. $\frac{2S}{b\rho g}\cos (\theta +\alpha /2)$

Answer 1

The correct option is D $\frac{2S}{b\rho g}\cos (\theta +\alpha /2)$


If $R$ be the meniscus radius
$R\cos (\theta +\alpha /2)=b$
Excess pressure on concave side of meniscus=$\frac{2S}{R}$
$h\rho g=\frac{2S}{R}=\frac{2S}{b}\cos (\theta +\alpha /2)$
$\Rightarrow h=\frac{2S}{b\rho g}\cos (\theta +\alpha /2)$