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,      \[{{r}_{1}}={{r}_{2}}=r\] \[\therefore \]  \[r=\frac{{{r}^{2}}}{0}=\infty \]