Question

A soap bubble of radius $R$ is surrounded by another soap bubble of radius $2R$, as shown. Take surface tension $=S$. Then the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be

• A. $\frac{4S}{R}$
• B. $\frac{3S}{R}$
• C. $\frac{6S}{R}$
• D. None of these

Answer 1

The correct option is C $\frac{6S}{R}$

Let, $P_0$ be the atmosphere pressure
$P_1$= pressure inside the soap bubble of radius 2R
$P_2$ = pressure inside the soap bubble of radius R
Excess in pressure for soap bubble of radius 2R
$P_1-P_0=\frac{4S}{2R}.....\left(1\right)$
Excess in pressure for soap bubble of radius R
$P_2-P_1=\frac{4S}{R}.....\left(2\right)$
Add (1) and (2),
$P_1-P_0+P_2-P_1=\frac{4S}{2R}+\frac{4S}{R}$
$=\frac{4S+8S}{2R}$
$P_2-P_0=\frac{6S}{R}$