Question

The angle of contact between glass and water is $0^{\circ }$ and water (surface tension $70dyn/cm$) rises in a glass capillary up to $6cm$. Another liquid of surface tension $140dyn/cm$, angle of contact ${60}^{\circ }$ and relative density $2$ will rise in the same capillary up to

• A. $12cm$
• B. $24cm$
• C. $3cm$
• D. $6cm$

Answer 1

The correct option is C $3cm$

The height $h$ through which a liquid will rise in a capillary tube of radius $r$ is given by $h=\frac{2S\cos \theta }{r\rho g}$

where $S$ is the surface tension, $\rho$ is the density of the liquid and $\theta$ is the angle of contact.

for same capillary and two liquids $\frac{h_1}{h_2}=\frac{2S_1\cos {\theta }_1}{r{\rho }_{1}g}\times \frac{r{\rho }_{2}g}{2S_2\cos {\theta }_2}\Rightarrow \frac{h_1}{h_2}=\frac{S_1\cos {\theta }_1}{{\rho }_1}\times \frac{{\rho }_2}{S_2\cos {\theta }_2}\Rightarrow \frac{6}{h_2}=\frac{70\times 1}{1}\times \frac{2}{140\times \left(1/2\right)}\Rightarrow h_2=3cm$