Physics - Fluid Question with Solution | TestHub

As volume of the bubble

v$=\frac{4}{3}\pi {\text{R}}^3\Rightarrow \text{R}={\left(\frac{3}{4\pi }\right)}^{1/3}{\text{V}}^{1/3}\Rightarrow {\text{R}}^2={\left(\frac{3}{4\pi }\right)}^{2/4}{\text{V}}^{2/3}$

$\Rightarrow {\text{R}}^2\alpha {\text{V}}^{2/3}$

Work done in blowing a soap bubble

$\text{W}=8\pi {\text{R}}^2\text{T}\Rightarrow \text{W}\propto {\text{R}}^2\propto {\text{V}}^{2/3}$

$\therefore \frac{{\text{W}}_2}{{\text{W}}_1}={\left(\frac{{\text{V}}_2}{{\text{V}}_1}\right)}^{2/3}={\left(\frac{2\text{V}}{\text{V}}\right)}^{2/3}={\left(2\right)}^{2/3}={\left(4\right)}^{1/3}\Rightarrow {\text{W}}_2=\sqrt[3]{4}\text{W}$