Question

A capillary tube of a uniform bore is dipped vertically in water which rises by 7cm in the tube.Find the radius of the capillary if surface tension in 70 dynes/cm,Take g=$9.8m/s^2$.

Answer 1

Given Rise in tube $h=7cm=7\times {10}^{-2}m$

Surface Tension $T=70dynes/cm.=70\times {10}^{-3}N/m$

Acceleration due to gravity $g=9.8m/s^2$

Density of water $p=1\times {10}^{34}g/m^3$

Angle of contact $\theta =0^0$

Radius of the tube $r=?$

The rise in tube is given by

$h=\frac{2T\cos \theta }{rpg}$

$r=\frac{2T\cos \theta }{hpg}$

$\therefore$ $r=\frac{(2\times 70\times {10}^{-3}\times \cos 0^0)}{7\times {10}^{-2}\times 1\times {10}^3\times 9.8}$

$\therefore$ $r=2\times {10}^{-4}m=0.2\times {10}^{-3}m=0.2m$