Question

A soap bubble has radius $R$ and thickness $d \, \left(\right. < < R\left.\right)$ as shown in the diagram. It collapses into a spherical drop. The ratio of excess pressure in the drop to the excess pressure inside the bubble is

• A. $\left(\frac{R}{3 d}\right)^{\frac{1}{3}}$
• B. $\left(\frac{R}{6 d}\right)^{\frac{1}{3}}$
• C. $\left(\frac{R}{24 d}\right)^{\frac{1}{3}}$
• D. None of these

Answer 1

Answer: (C)

The volume of soap solution in a bubble $=4\pi R^{2}d$
now we make a drop
$4\pi \left(\textit{R}\right)^{2}\textit{d}=\frac{4}{3}\pi \left(\textit{r}\right)^{3}\Rightarrow \textit{r}=\left(3 \left(\textit{R}\right)^{2} \textit{d}\right)^{1 / 3}$
Excess pressure initially $=\frac{4 \textit{S}}{\textit{R}}$
Excess pressure finally $=\frac{2 \textit{S}}{\textit{r}}=\frac{2 \textit{S}}{\left(3 \left(\textit{R}\right)^{2} \textit{d}\right)^{1 / 3}}$
Ratio $=\left(\frac{\textit{R}}{24 \textit{d}}\right)^{\frac{1}{3}}$