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