Question

A soap bubble has radius $R$ and thickness $d(<<R)$ 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. ${\left(\frac{R}{3d}\right)}^{\frac{1}{3}}$
• B. ${\left(\frac{R}{6d}\right)}^{\frac{1}{3}}$
• C. ${\left(\frac{R}{24d}\right)}^{\frac{1}{3}}$
• 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
$4\pi {\left(\text{R}\right)}^2\text{d}=\frac{4}{3}\pi {\left(\text{r}\right)}^3\Rightarrow \text{r}={\left(3{\left(\text{R}\right)}^2\text{d}\right)}^{1/3}$
Excess pressure initially $=\frac{4\text{S}}{\text{R}}$
Excess pressure finally $=\frac{2\text{S}}{\text{r}}=\frac{2\text{S}}{{\left(3{\left(\text{R}\right)}^2\text{d}\right)}^{1/3}}$
Ratio $={\left(\frac{\text{R}}{24\text{d}}\right)}^{\frac{1}{3}}$