Q. Let $W$ be the work done, when a bubble of volume $V$ is formed from a given solution. How much work is required to be done to form a bubble of volume 2 $V$?
A) $W$
B) $2W$
C) $2^{1/3}\ W$
D) $4^{1/3}\ W$
Explanation
(d) Let $R$ and $R'$ be the radius of bubble of volume $V$ and $2\ V$ respectively. Then
$\frac{4}{3}\pi{\ R}^{3} = V$ and $\frac{4}{3}\pi R^{'3} = 2V$
So, $\frac{R^{'3}}{R^{3}} = 2$ or $R^{'} = (2)^{1/3}R$
As $W = S \times (4\ \pi R^{2})2$ and $W^{'} = S \times (4\ \pi\ R^{'2})2$
$\frac{W^{'}}{W} = \frac{R^{'2}}{R^{2}} = 2^{2/3} = (4)^{1/3}$ or $W^{'} = (4)^{1/3}W$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.