Question

A bowl whose bottom has round holes of diameter $1mm$ is filled with water. Assuming that surface tension acts only at holes, find the maximum height (in $cm$ ) up to which water can be filled in the vessel without leakage. (Given, surface tension of water $=75\times 10^{-3}N{m}^{-1},g=10m{s}^{-2}$ and density of water $=1g/c{m}^3$.

Answer 1

Answer: 3

The vertical force due to surface at the hole

$=T\cos \theta \times L=T\cos \theta \times 2\pi r$
This will balance weight $mg\left(=\pi r^{2}h\rho g\right)$
$\therefore T\cos \theta \times 2\pi r=\pi r^{2}h\rho g$
$\Rightarrow h=\frac{2T\cos \theta }{r\rho g}$
$h$ is maximum, when $\cos \theta =1$
$\therefore h_{\max }=\frac{2T}{r\rho g}=\frac{2\times 0.075}{0.0005\times 1000\times 10}$
$=0.03m=3cm$