Question

A vessel, whose bottom has round holes with diameter $0.1mm$, is filled with water. The maximum height up to which water can be filled without leakage is

• A. $100cm$
• B. $75cm$
• C. $50cm$
• D. $30cm$

Answer 1

The correct option is D $30cm$

For equilibrium,
Total upward force by surface tension
$=$ Weight of the water in tube
$\Rightarrow \pi \times D\times$ surface tension (circumference)
$=\pi (D/2{)}^2\times h\times density\times g$ (cross section)
where $D\left(diameter\right)=0.1mm=0.01cm$
Density of water $=1\times {10}^{-3}g/c{m}^3$
$\Rightarrow \pi \times \left(0.01\right)\times 75\times {10}^{-3}$
$=\pi \times {\left(\frac{0.01}{2}\right)}^2\times h\times 1\times {10}^{-3}\times 1000$
$\therefore h=\frac{0.75\times 0.01\times 4}{0.01\times 0.01}=0.3m=30cm$.