Question

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

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

Answer 1

The correct option is C $\frac{6S}{4}$

Let the pressure inside smaller soap bubble be $P_2$, bigger soap bubble be $P_1$ and atmospheric pressure be $P_o$

Excess pressure across bigger soap bubble and atmosphere,
$\begin{array}{}{P}_1-P_o=\frac{4S}{2R}=\frac{2S}{R}& \text{(1)}\end{array}$
where $S$ is the surface tension.
Excess pressure across bigger bubble and smaller bubble,
$\begin{array}{}{P}_2-P_1=\frac{4S}{R}& \text{(2)}\end{array}$
Adding $\left(1\right)$ and $\left(2\right)$
$P_2-P_o=\frac{6S}{R}$
Hence pressure inside smaller soap bubble in excess of atmospheric pressure is $\frac{6S}{R}$