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)

$192\pi r^{2}T$

Answer 2

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