Question

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

• A. 3 cm
• B. 0.3 cm
• C. 3 mm
• D. 3 m

Answer 1

Answer: (A)

The height $(h)$ to which water rises in a capillary is
$h=\frac{2T\cos \theta }{r\rho g}$
Where $T$ is surface tension,
$r$ the radius of capillary,
$p$ the density and
$g$ the acceleration due to gravity.
For maximum height $\theta =0$
$\therefore \cos \theta =1$
$\Rightarrow h=\frac{2T}{r\rho g}$
Given, $R=\frac{1}{2}mm=\frac{10^{-3}}{2}md=10^{3}kg/m^3$
$h=\frac{2\times 75\times 10^{-3}\times 2}{10^{-3}\times 10^3\times 10}m$ $\Rightarrow h=3\times 10^{-2}m$
$\Rightarrow h=3cm$