Q155 / 200 · Manipal (MET) 2014 · Physics
Several spherical drops of a liquid of radius $r$ coalesce to form a single drop to radius $R$. If $T$ is surface tension and $V$ is volume under consideration, then the release of energy is
- A$3 V T\left(\frac{1}{r}+\frac{1}{R}\right)$
- Correct answerB$3 V T\left(\frac{1}{r}-\frac{1}{R}\right)$
- C$V T\left(\frac{1}{r}-\frac{1}{R}\right)$
- D$V T\left(\frac{1}{r^2}+\frac{1}{R^2}\right)$
Solution
Energy released
$\begin{aligned}
& =4 \pi T R^3\left(\frac{1}{r}-\frac{1}{R}\right)=3\left(\frac{4}{3} \pi R^3\right) T\left(\frac{1}{r}-\frac{1}{R}\right) \\
& =3 V T\left(\frac{1}{r}-\frac{1}{R}\right)
\end{aligned}$
Hence, the correct answer is option: 'B'.