Question

If two soap bubbles of equal radii $r$ coalesce, then the radius of curvature of interface between two bubbles will be

• A. r
• B. zero
• C. infinity
• D. $\frac{1}{2r}$

Answer 1

Answer: (C)

Let radius of curvature of the common internal film surface of the double bubble formed be $r$.
Then, excess of pressure as compared to atmosphere inside $A$ is
$\frac{4T}{r_1}$ and $B$ is $\frac{4T}{r_2}$.
The pressure difference is
$\frac{4T}{r_1}-\frac{4T}{r_2}=\frac{4T}{r^{\prime }}$
$\Rightarrow r^{\prime }=\frac{r_1{r}_2}{r_2-r_1}$
Given, $r_1=r_2=r$
$\therefore r^{\prime }=\frac{r^2}{0}=\infty$