Question

A small hollow sphere, which has a small hole in it, is immersed in water to a depth of 0.5 m before any drop penetrates into it. If surface tension for water is 0.073 N/m, the radius of the hole is

• A. 0.06 mm
• B. 0.03 mm
• C. 0.09 mm
• D. 0.15 mm.

Answer 1

The correct option is B 0.03 mm

Under Equilibrium condition the pressure treated by water would be equal to the excuse pressure inside the bubble

So, $\frac{2T}{r}=hpg\Rightarrow r=\frac{2T}{hpg}$

$T=0.075n/m$

$h=40cm=0.4m$

$p=1000kg/m^3$

$g=9.8$

$\therefore r=\frac{2\times 0.075}{0.4\times 1000\times 9.8}=\frac{0.15}{3924}$

$\therefore r=3.8\times {10}^{-5}m$