Question

A large vessel having a very small circular hole of diameter $1mm$ at the bottom is filled with water. Up to what maximum height (in $cm$ ) water can be filled in the vessel so that there is no leakage? [surface tension of water $=7.5\times 10^{- 2} \, Nm^{- 1} \, $ and $g=10ms^{- 2}$ ]

Answer 1

Water will not leak out from the hole if the weight of water in the water column is supported by the force due to surface tension.
Using the relation,
$h=\frac{2 T}{r \rho g}$
$=\frac{2 \times 7.5 \times 10^{- 2}}{0.5 \times 10^{- 3} \times 10^{3} \times 10}$
$=3\times 10^{- 2} \, m=3 \, cm$