The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of…

The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of first bubble to other is
  1. $1:3$
  2. $1:9$
  3. $27:1$
  4. $1:27$

Solution

$\begin{aligned} & \quad \Delta \mathrm{P} \propto \frac{1}{\mathrm{r}} \Rightarrow \frac{\mathrm{r}_1}{\mathrm{r}_2}=\frac{\Delta \mathrm{P}_2}{\Delta \mathrm{P}_1}=\frac{1}{3} \\ & \therefore \quad \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{1}{27}\end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 1)

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