Question

A container, whose bottom has round holes with diameter $o.1mm$ is filled with water. The maximum height in $cm$ upto which water can be filled without leakage will be what?
Surface tension= $75\times {10}^{-3}N/m$ and $g=10m{s}^{-2}$:

• A. $20cm$
• B. $40cm$
• C. $30cm$
• D. $60cm$

Answer 1

The correct option is C $30cm$

When the maximum height of water is reached.
Surface tension force=hydrostatic force
$\Rightarrow T\left(2\pi r\right)=h{\rho }_{w}g\left(\pi r^2\right)\Rightarrow h=\frac{2T}{{\rho }_{w}gr}=\frac{2\times 75\times {10}^{-3}}{1000\times 10\times 0.05\times {10}^{-3}}=0.3m=30cm$