Question

A vessel, whose bottom has round holes with diameter $0.1\text{mm}$, is filled with water. The maximum height (in $\text{cm}$) up to which water can be filled without leakage is
(Take Surface Tension due to water as $75\frac{\text{dyne}}{\text{cm}},$acceleration due to gravity $g=1000\frac{\text{cm}}{{\text{s}}^2}$)

Answer 1

Given
$D$ (diameter) $=0.1\text{mm}=0.01\text{cm}$
Density of water $\rho =1{\text{g/cm}}^3$
Surface Tension due to water is $75\frac{\text{dyne}}{\text{cm}}$
Total upward force by surface tension = Weight of the water in tube
$\Rightarrow \pi \times D\times T=\pi (D/2{)}^2\times h\times \rho \times g$



$\Rightarrow \pi \times \left(0.01\right)\times 75=\pi \times {\left(\frac{0.01}{2}\right)}^2\times h\times 1\times 1000$
$\therefore h=\frac{0.075\times 0.01\times 4}{0.01\times 0.01}=0.3\text{m}=30\text{cm}$