Question

A soap bubble of radius $3 \,cm$ is formed inside the another soap bubble of radius $6 \,cm$. 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

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
$\Delta P =\frac{4 S }{ R _{\text{eq} }} \ldots$ (ii)
From (i) & (ii)
$\frac{4 S }{ R _{\text{eq}}}=\frac{4 S }{ r _{1}}+\frac{4 S }{ r _{2}}$
$\frac{1}{ R _{\text{eq}}}=\frac{1}{ r _{1}}+\frac{1}{ r _{2}}$
$=\frac{1}{6}+\frac{1}{3}$
$R _{\text{eq}}=2 \,cm$