A) 1 : 4
B) 1 : 2
C) 2 : 1
D) 4 : 1
Correct Answer: A
Solution :
Excess pressure in a soap bubble is given by \[P=\frac{4T}{R}=\Rightarrow P\propto \frac{1}{R}\] Hence, \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\] Given: \[{{P}_{1}}=4{{P}_{2}}\] \[\frac{4{{P}_{2}}}{{{P}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\Rightarrow \frac{{{R}_{2}}}{{{R}_{1}}}=4\Rightarrow \frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{4}=1:4\]
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