Question

Given, the work done in blowing a bubble against surface tensional forces of volume V is W. Then find the work done in blowing the bubble of volume 2V from the same soap solution.

• A. $\frac{W}{4}$
• B. $\sqrt{3}W$
• C. $\sqrt[3]{32}W$
• D. $\sqrt[3]{34}W$

Answer 1

The correct option is D $\sqrt[3]{34}W$

As volume of the bubble $V=\frac{4}{3}\pi R^3\Rightarrow R={\left(\frac{3}{4\pi }\right)}^{1/3}{V}^{1/3}\Rightarrow R^2={\left(\frac{3}{4\pi }\right)}^{2/3}{V}^{2/3}\Rightarrow R^2\propto V^{2/3}$
Work done in blowing a soap bubble $W=8\pi R^{2}T\Rightarrow W\propto R^2\propto V^{2/3}$
$\therefore \frac{W_2}{W_1}={\left(\frac{V_2}{V_1}\right)}^{2/3}={\left(\frac{2V}{V}\right)}^{2/3}=(2{)}^{2/3}=(4{)}^{1/3}\Rightarrow W_2=\sqrt[3]{34}W$