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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids2 Marks
Question
The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio between the volume of the first and the second bubble?
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Answer

Given, $\frac{\text{4T}}{\text{r}_1}=\frac{3\times4\text{T}}{\text{r}_2}$ or $r_2 = 3r_1 \frac{\text{V}_1}{\text{V}_2}=\frac{\Big(\frac43\Big)\pi\text{r}_1^3}{\Big(\frac43\Big)\pi\text{r}^3_2}$
$=\Big(\frac{\text{r}_1}{\text{r}_2}\Big)^3=\Big(\frac{1}{3}\Big)^3=\frac{1}{27}$

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