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Pressure inside two soap bubbles are 1.01atm and 1.02atm respectively. The ratio of their volumes are

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a

4 :1

b

8 :1

c

2 :1

d

0.8 :1

answer is C.

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Detailed Solution

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$\begin{array}{l} ΔP = P - P_{0} = \frac{4 T}{R} \Rightarrow {ΔP}_{1} = 0 .01 atm \\ \Rightarrow {ΔP}_{2} = 0 .02 atm \\ \frac{{ΔP}_{1}}{{ΔP}_{2}} = \frac{4 T / R_{1}}{4 T / R_{2}} = \frac{R_{2}}{R_{1}} \\ \Rightarrow \frac{0 .01}{0 .02} = \frac{R_{2}}{R_{1}} \\ \Rightarrow \frac{V_{1}}{V_{2}} = {(\frac{R_{1}}{R_{2}})}^{3} = \frac{8}{1} \end{array}$

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