The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is

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Solution

Q.
The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is [2024]

1 1 : 9

2 1 : 3

3 1 : 81

4 1 : 27

Ans.
(4)

Excess pressure in soap bubble $= \frac{4 S}{R}$

Given $P_{1} = 3 P_{2}$ $∴$ $P_{1} = \frac{4 S}{R_{1}} and P_{2} = \frac{4 S}{R_{2}}$

$3 P_{2} = \frac{4 S}{R_{1}}; R_{1} = \frac{4 S}{3 P_{2}}; R_{2} = \frac{4 S}{P_{2}}$

$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{4 S}{3 P_{2}} \times \frac{P_{2}}{4 S} = \frac{1}{3}$

Ratio between the volumes $\frac{V_{1}}{V_{2}} = \frac{\frac{4}{3} π R_{1}^{3}}{\frac{4}{3} π R_{2}^{3}} = \frac{1}{27}$

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