Question

If a 5 cm long capillary tube with 0.1 mm internal diameter, open at both ends, is slightly dipped in water having surface tension 75 dyne/cm, state whether: water will rise halfway in the capillary?

Answer 1

$T=75dyne/㎝$

Radius, $r=\frac{0.1}{2}㎜=0.05㎜=0.005㎝$

Density, $\rho =1ℊ/㎤$ Angle of contact,$\theta =0°$

Let h be the height to which water rise in the capillary.

We know that, $h=\frac{2T\cos \theta }{r\rho g}=\frac{2\times 75\times \cos \theta °}{0.005\times 1\times 981}㎝$

$h=30.58㎝$

But length of capillary tube $h^{\prime }=5㎝$

Because $h>\frac{h^{\prime }}{2}$, hence water will not rise halfway in the capillary. This possibility does not exist.