Question

A liquid drop of radius R breaks into 64 tiny drops each of radius r. If the surface tension of the liquid is T, then the gain in energy is

• A. $48\pi R^{2}T$
• B. $12\pi r^{2}T$
• C. $96\pi R^{2}T$
• D. $192\pi r^{2}T$

Answer 1

Answer: (D)

Volume of big drop = 64 $\times$ volume of tiny drops or $\frac{4}{3}\pi R^3=64\times \frac{4}{3}\pi r^3$ or $R=4r$ So, the gain in surface energy = work done in splitting a liquid drop of radius R into n identical drops $=4\pi T{R}^2(n^{1/3}-1)$ $=4\pi T{(4r)}^2({64}^{1/3}-1)=192\pi r^{2}T$