Excess pressure in soap bubble \(=\frac{4 S}{R}\)

\(P=\frac{4 S}{R}\)   \(\left\{\begin{array}{l}S \text { - Surface tension } \\ R \text { - Radius }\end{array}\right.\)

For second bubble,

\(2 P=\frac{4 S}{x}\)   \(\left\{\begin{array}{l}S \text { - Surface tension } \\ R \text { - Radius }\end{array}\right.\)

Substitute value of \(P\)

\(2 \times \frac{4 S}{R}=\frac{4 S}{x}\)

\(\Rightarrow x=\frac{R}{2}\)

Ratio of Radii \(=\frac{R / 2}{R}=\frac{1}{2}\)

So, Ratio of volume \(=\left(\right.\) Ratio of Radii )\(^3\)

\(=\left(\frac{1}{2}\right)^3=\frac{1}{8}\)