Question

A container, whose bottom has round holes with diameter $0.1mm$ is filled with water. The maximum height in cm upto which water can be filled without leakage will be what ?
$Surfacetension=75\times {10}^{-3}N/m$ and $g=10m/s^2$ :

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

Answer 1

The correct option is C $30cm$

Given : $T=75\times {10}^{-3}N/m$ $g=10m/s^2$ $\rho =1000kg/m^3$

Radius $r=\frac{d}{2}=\frac{0.1}{2}=0.05mm=0.05\times {10}^{-3}m$

Height raised $h=\frac{2T}{\rho gr}$

$⟹$ $h=\frac{2\times 75\times {10}^{-3}}{1000\times 10\times 0.05\times {10}^{-3}}=0.3m=30cm$