Question

If the work done in blowing a bubble of volume V is W, then the work done in blowing the bubble of volume 2V from the same soap solution will be

• A. W/2
• B. $\sqrt{2}W$
• C. $\sqrt[3]{2}$W
• D. $\sqrt[3]{4}$W

Answer 1

Answer: (D)

$\sqrt[3]{4}$W

Answer 2

As volume of the bubble $V = \frac{4}{3}\pi R^{3}$ ⇒ $R = \left( \frac{3}{4\pi} \right)^{1/3}V^{1/3}$ ⇒ $R^{2} = \left( \frac{3}{4\pi} \right)^{2/3}V^{2/3}$ ⇒ $R^{2} \propto V^{2/3}$

Work done in blowing a soap bubble $W = 8\pi R^{2}T$ ⇒ $W \propto R^{2} \propto V^{2/3}$

∴$\frac{W_{2}}{W_{1}} = \left( \frac{V_{2}}{V_{1}} \right)^{2/3} = \left( \frac{2V}{V} \right)^{2/3} = (2)^{2/3} = (4)^{1/3} \Rightarrow W_{2} = \sqrt[3]{4}W$