Question

There is a small hole in a hollow sphere. When it is taken to a depth of $20cm$ under water, water enters in it. If the surface tension of water is $0.07N/m$, the radius of the hole in $\mu m$ is______.
(Take $g=10m/s^2$ )

Answer 1

Answer: 70

When water enters the hollow sphere, force of surface tension is balanced by normal force exerted by the liquid column,
i.e., $T\times 2\pi r=\pi r^{2}h\rho g$
where, $r$ is radius of hole of the sphere.
$\therefore r=\frac{2T}{h\rho g}=\frac{2\times 0.07}{20\times 10^{-2}\times 10^3\times 10}$
$=70\times 10^{-6}m$
$\therefore r=70\mu m$