Question

Work W is required to be done to form a spherical bubble of volume V from a given soap solution. How much work is needed to form a spherical bubble of volume 2V?

• A. 2 W
• B. $\sqrt{2}W$
• C. $\left(2^{1/3}\right)W$
• D. $\left(4^{1/3}\right)W$

Answer 1

The correct option is D

$\left(4^{1/3}\right)W$

$W=8\pi r^2\sigma .$ Now $V=\frac{4}{3}\pi r^3.$ Hence

$W=8\pi \sigma {\left(\frac{3V}{4\pi }\right)}^{2/3},i.e.W\alpha V^{2/3}$