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 \[\Delta {{P}_{1}}=1.01-1=0.01\,atm\] Inside bubble \[B\] is \[\Delta {{P}_{2}}=1.03-1=0.03\,atm\] 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 \[P=\frac{4T}{r}\] \[\therefore \]Let \[{{r}_{1}}\] and \[{{r}_{2}}\] be the radii of bubbles\[A\,and\,B\]respectively, then \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{4T/{{r}_{1}}}{4T/{{r}_{2}}}=\frac{0.01}{0.03}\] \[\Rightarrow \] \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{3}\] Since, bubbles are spherical in shape, their volume?s are in the ratio \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{2}\,\pi \,r_{1}^{3}}{\frac{4}{2}\,\pi \,r_{2}^{3}}\] \[={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{3}{1} \right)}^{3}}=\frac{27}{1}\] \[\Rightarrow \] \[{{V}_{1}}:{{V}_{2}}=27:1\]
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