A) 102 : 101
B) \[{{(102)}^{3}}\text{:(}103{{)}^{3}}\]
C) 8 : 1
D) 2 : 1
Correct Answer: C
Solution :
Let \[{{r}_{1}}\] and \[{{r}_{2}}\] be the radii of two soap bubbles. Excess pressure inside first soap bubble \[\frac{4T}{{{r}_{1}}}=1.01-1=0.01\] atm Excess pressure inside second soap bubble \[\frac{4T}{{{r}_{2}}}=1.02-1=0.02\] atm Therefore, \[\frac{4T/{{r}_{1}}}{4T/{{r}_{2}}}=\frac{0.01}{0.02}=\frac{1}{2}\] \[\Rightarrow \] \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{2}\] The ratio of their volumes is given by \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{3}\pi {{r}_{1}}^{3}}{\frac{4}{3}\pi r_{2}^{3}}\] \[\Rightarrow \] \[\frac{{{V}_{1}}}{{{V}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\] \[={{\left( \frac{2}{1} \right)}^{3}}\]
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