Question

Water rise in capillary tube when is one end is dipped vertically in it, is $3cm$. If the surface tension of water is $75\times {10}^{-3}N/m$, then the diameter (in $mm$) of capillary will be (Take angle of contact $=0^{\circ }$)

Answer 1

The relation between height of water column in capillary tube and radius of capillary tube is

$h=\frac{2T\cos \theta }{r\rho g}$

$h=\frac{2T\cos \theta }{r\rho g}$ or $r=\frac{2T\cos \theta }{h\rho g}$

Here, $T=75\times {10}^{-3}N/m$ and $h=3cm,\rho =1000kg/m^3,\theta =0^{\circ },g=10m/s^2$

$r=\frac{2\times 75\times {10}^{-3}\times \cos 0^{\circ }}{3\times {10}^{-2}\times {10}^3\times 10}m$

$=5\times {10}^{-4}m=0.5mm$