A) \[27:1\]
B) \[3:1\]
C) \[127:101\]
D) None of these
Correct Answer: A
Solution :
Excess pressure as compared to atmosphere inside bubble A is \[\Delta {{p}_{1}}=1.01-1=0.01\text{ }atm\] inside bubble B is \[\Delta {{p}_{2}}=1.03-1=0.03\text{ }atm\] Also when radius of a bubble is r, formed from a solution whose surface tension is t, then excess pressure inside the bubble is given by \[p=\frac{4t}{r}\] Let\[{{r}_{1}}\]be the radii of bubbles A and B respectively then \[\frac{{{p}_{1}}}{{{p}_{2}}}=\frac{4T/{{r}_{1}}}{4T/{{r}_{2}}}=\frac{0.01}{0.03}\] \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{3}\] Since bubbles are spherical in shape their volumes are in the ratio \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{2}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}\] \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{3}{1} \right)}^{3}}=\frac{27}{1}\] \[{{V}_{1}}:{{V}_{2}}=27:1\]
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