Question

When a long glass capillary tube of radius $0.015\text{cm}$ is dipped in a liquid, the liquid rises to a height of $15\text{cm}$ within it. If the contact angle between the liquid and glass to close to $0^{\circ },$ the surface tension of the liquid (in ${\text{mN m}}^{-1}$) is ______.
(Give answer in the closest integer)

[${\rho }_{\text{(liquid)}}=900{\text{kg m}}^{-3},g=10{\text{ms}}^{-2}$]

Answer 1

Given,
$r=0.015\text{cm}=15\times {10}^{-5}\text{m}$
$h=15\text{cm}=15\times {10}^{-2}\text{m}$

Capillary rise is given by,

$h=\frac{2T\cos \theta }{\rho gr}[\cos \theta =\cos 0^{\circ }=1]$
$\Rightarrow T=\frac{rh\rho g}{2}=\frac{15\times {10}^{-5}\times 15\times {10}^{-2}\times 900\times 10}{2}$
$=101.25\times {10}^{-3}{\text{N m}}^{-1}\approx 101{\text{mN m}}^{-1}$