Question

A soap bubble of radius $3cm$ is formed inside the another soap bubble of radius $6cm$. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is _____ $cm$.

Answer 1

Answer: 2

Excess pressure inside the smaller soap bubble
$\Delta P=\frac{4S}{r_1}+\frac{4S}{r_2}.....$ (i)
The excess pressure inside the equivalent soap bubble
$\Delta P=\frac{4S}{R_{\text{eq}}}\dots$ (ii)
From (i) & (ii)
$\frac{4S}{R_{\text{eq}}}=\frac{4S}{r_1}+\frac{4S}{r_2}$
$\frac{1}{R_{\text{eq}}}=\frac{1}{r_1}+\frac{1}{r_2}$
$=\frac{1}{6}+\frac{1}{3}$
$R_{\text{eq}}=2cm$