Question

A capillary tube made of glass of radius $0.15\text{mm}$ is dipped vertically in a beaker filled with methylene iodide (surface tension $=0.05{\text{Nm}}^{-1}$, density $=667{\text{kg m}}^{-3}$ ) which rises to height $h$ in the tube. It is observed that the two tangents drawn from liquid-glass interface (from opp. sides of the capillary) make an angle of ${60}^{\circ }$ with one another. Then $h$ is close to ($g=10{\text{ms}}^{-2}$).

• A. $0.049\text{m}$
• B. $0.087\text{m}$
• C. $0.137\text{m}$
• D. $0.172\text{m}$

Answer 1

The correct option is B $0.087\text{m}$

Given,
Angle of contact $\theta ={30}^{\circ }$
Surface tension $T=0.05{\text{Nm}}^{-1}$
Radius of capillary tube $r=0.15\text{mm}=0.15\times {10}^{-3}\text{m}$
Density of methylene iodide $\rho =667{\text{kg m}}^{-3}$


Capillary rise, $h=\frac{2T\cos \theta }{\rho gr}$

$h=\frac{2\times 0.05\times \frac{\sqrt{3}}{2}}{667\times 10\times 0.15\times {10}^{-3}}=0.087\text{m}$