Question

What should be the radius of a capillary tube if water has to raise to a height of 6 cm in it? (Surface tension of water = 7.2 × 10⁻² N m⁻¹)

Answer 1

Height of liquid in the capillary tube is given by, $h=\frac{2Scos\theta}{\rho rg}$

where S is surface tension of liquid.
$\rho$ is density of liquid.
r is the radius of capillary tube.
g is acceleration due to gravity.
and $\theta$ is angle of contact.

here, $\theta=0^{\circ}$ [ angle of contact becomes zero for water ]
g = 9.8 m/s², h = 6cm and S = 7.2 × 10^-2 N/m

now, 6cm = {2 × 7.2 × 10^-2 N/m cos0°}{1000 kg/m³ × 9.8 m/s² × r}

or, r = 0.144/{1000 × 9.8 × 6 × 10^-2 }

r = 0.144/98 × 6 = 0.0002448 m

r = 2.448 × 10^-4 m