Question

A vessel whose bottom has round hole with diameter of $1mm$ is filled with water. Only surface tension acts at hole. (Surface tension of water is $75\times {10}^{-3}$ N/m and $g=10m/s^2$). The maximum height (in $cm$) to which water can be filled in the vessel without leakage is:

• A. $2$
• B. $3$
• C. $4$
• D. $1$

Answer 1

Answer: (B)

$3$

The vertical force due to surface tension at the whole is
($T\cos \theta )L=(T\cos \theta )2\pi r$
and it would balance the weight mg of the drop
$m=\pi r^2\rho h$

$\Rightarrow T\cos \theta \left(2\pi r\right)=\pi r^{2}h\rho g$
$\Rightarrow h=\frac{2Tcos\theta }{\rho rg}$

$h$ is maximum when $\cos \theta =1$
$\Rightarrow h_{max}=\frac{2\times 75\times {10}^{-3}}{{10}^3\times 5\times {10}^{-4}\times 10}$
$=0.03m$
$=3cm$