question_answer

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)  \[\frac{1}{2r}\]

Correct Answer: C

Solution :

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 \[\frac{4T}{{{r}_{1}}}-\frac{4T}{{{r}_{2}}}=\frac{4T}{r'}\Rightarrow \,\,r'=\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{2}}-{{r}_{1}}}\] Given,         \[{{r}_{1}}={{r}_{2}}=r\] \[\therefore \] \[r'=\frac{{{r}^{2}}}{0}=\infty \]