A) \[{{r}_{2}}-{{r}_{1}}\]
B) \[\sqrt{r_{1}^{2}-r_{2}^{2}}\]
C) \[\frac{{{r}_{1}}+{{r}_{2}}}{2}\]
D) \[\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}-{{r}_{2}}}\]
Correct Answer: D
Solution :
Key Idea: Excess pressure inside \[a\] bubble of radius \[R\] is given by\[P=\frac{4T}{r}\]. Let \[{{P}_{1}}\] and \[{{P}_{2}}\] are pressure differences across the common interface. Let \[r\] is radius of curvature of the common surface. \[{{P}_{2}}-{{P}_{1}}=\frac{4T}{r}\] \[\frac{4T}{r}=\frac{4T}{{{r}_{2}}}=\frac{4T}{{{r}_{1}}}(T=\]surface tension) \[\frac{1}{r}=\frac{1}{{{r}_{2}}}-\frac{1}{{{r}_{1}}}\] \[r=\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}-{{r}_{2}}}\]You need to login to perform this action.
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