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, the 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 $\theta$, then the value of $h$ will be ($g$ is the acceleration due to gravity)

• A

  $\frac{2S}{b\rho g}\cos (\theta -\alpha )$
• B

  $\frac{2S}{b\rho g}\cos \left(\theta +\alpha \right)$
• C

  $\frac{2S}{b\rho g}\cos \left(\theta -\frac{\alpha }{2}\right)$
• Correct answer
  D

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

Hence, the correct answer is option: 'D'.