1 \(4VT\left( {\frac{1}{r} - \frac{1}{R}} \right)\) is released
2 \(3VT\left( {\frac{1}{r} - \frac{1}{R}} \right)\) is released
3 \(3VT\left( {\frac{1}{r} + \frac{1}{R}} \right)\) is absorbed
4 Energy is neither released nor absorbed
Explanation:
Let \(R\) is the radius of the bigger drop and \(N\) drops are combined to form the bigger drop.
\(N \dfrac{4}{3} \pi r^{3}=\dfrac{4}{3} \pi R^{3}\)
\(N{r^3} = {R^3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
The energy released
\(E=T\left[A_{i}-A_{f}\right]\)
\(E=T\left[N 4 \pi r^{2}-4 \pi R^{2}\right]\)
\(=4 \pi R^{2} T\left[\dfrac{N r^{2}}{R^{2}}-1\right]\)
\( = 3\left( {\frac{4}{3}\pi {R^3}} \right)T\left[ {\frac{{N{r^2}}}{{{R^3}}} - \frac{1}{R}} \right]\)
\(=3 V T\left[\dfrac{1}{r}-\dfrac{1}{R}\right]\)