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 \[\Delta {{p}_{2}}=1.03-1\] \[=0.03\,\text{atm}\] \[\rho =\frac{4T}{r}\] Let \[{{r}_{1}}\]and \[{{r}_{2}}\]be the radii of bubbles A and 8 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 \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{4/3\pi r_{1}^{3}}{4/3\pi r_{2}^{3}}\] \[\frac{{{V}_{1}}}{{{V}_{2}}}={{\left( \frac{3}{1} \right)}^{3}}\] \[=\frac{27}{1}\] \[{{v}_{1}}:{{v}_{2}}=27:1\]
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