Discussion Forum



1)

A glass capillary tube is of the shape of a truncated cone with an apex angle  $\alpha$  so that its two ends have cross-sections of different radii. When dipped in water vertically, water rises in its height h, where the radius of its cross-section in b. If the4 surface tension of water is S.  its density is ρ, and its contact angle with glass is θ, the value of h will be (g is the acceleration due to gravity)

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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:

Option D

Explanation:

Using geometry 

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$\frac{b}{R}=\cos(\theta+\frac{\alpha}{2})$

$\Rightarrow $   $ R=\frac{b}{\cos(\theta+\frac{\alpha}{2})}$

  Using pressure  equation along the path MNTK

$p_{0}-\frac{2S}{R}+h\rho g=p_{0}$

 Substituting the value of R , we get 

           $h=\frac{2S}{R\rho g}$

         $=\frac{2S}{b\rho g}\cos(\theta+\frac{\alpha}{2})$