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The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of volumes is (atmospheric pressure=1atm = $10^{5} P a$ )

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1:1

8:1

2:3

3:5

answer is B.

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Detailed Solution

$Δ P = \frac{4 T}{R} 1.02 - 1 = \frac{Δ T}{R_{2}} 0.02 - 1 = \frac{Δ T}{R_{2}}$

$\Rightarrow 1.01 - 1 = \frac{Δ T}{R_{1}} \Rightarrow 0.01 = \frac{Δ T}{R_{1}}$

Similarly

$R_{2} = \frac{Δ T}{0.02}$

$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{2}{1} \Rightarrow \frac{V_{1}}{V_{2}} = {(\frac{R_{1}}{R_{2}})}^{3} = {(\frac{2}{1})}^{3} = \frac{8}{1} \Rightarrow 8 : 1$

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