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 ii identical drops
$=4\pi T{R}^2\left(n^{1/3}-1\right)$
$=4\pi T(4r{)}^2\left(64^{1/3}-1\right)$
$=192\pi r^{2}T$