Question

A liquid rises in glass capillary tube up to a height of 2.5 cm at room temperature. If another glass capillary tube having radius half that of the earlier tube is immersed in the same liquid, the rise of liquid in it will be ______.

• A. 1.25 cm
• B. 2.5 cm
• C. 5 cm
• D. 10 cm

Hint:

Capillary rise is inversely proportional to tube radius; use \( h = \frac{2T \cos \theta}{\rho g r} \).

Answer 1

The Correct Option is C

Capillary rise formula: \( h = \frac{2T \cos \theta}{\rho g r} \), where \( T \) is surface tension, \( \theta \) is contact angle, \( \rho \) is density, \( g \) is gravity, and \( r \) is radius.
Height is inversely proportional to radius: \( h \propto \frac{1}{r} \).
If radius is halved (\( r' = \frac{r}{2} \)):
\[ h' = \frac{h \cdot r}{r/2} = 2h = 2 \cdot 2.5 = 5 \, \text{cm}. \] Answer: 5 cm.