Question

A small soap bubble of radius $4cm$ is trapped inside another bubble of radius $6cm$ without any contact. Let $P_2$ be the pressure inside the inner bubble and $P_0$, the pressure outside the outer bubble. Radius of another bubble with pressure difference $P_2-P_0$ between its inside and outside would be

• A. $6cm$
• B. $12cm$
• C. $4.8cm$
• D. $2.4cm$

Answer 1

The correct option is D $2.4cm$

As we enter a soap bubble the pressure increases by $\frac{4T}{R}$

Here $R$ is radius of bubble,and $T$ is surface tension.

$P_2=P_0+\frac{4T}{4}+\frac{4T}{6}$

$p_2=P_0+\frac{5}{12}\times 4T$

$P_2-P_0=\frac{4T}{\frac{12}{5}}$

So for a single bubble to have a pressure difference of $P_2-P_0$

$R=\frac{12}{5}=2.4cm$