c
Let \(n\) droplets each of radius \(r\) coalesce to form a big drop of radius \(R\).

\(\therefore \,\,Volume\,of\,n\,droplets = Volume\,of\,big\,drop\)

\(n \times \frac{4}{3}\pi {r^3} = \frac{4}{3}\pi {R^3} \Rightarrow n = \frac{{{R^3}}}{{{r^3}}}\)             \(...\left( i \right)\)

\(Volume\,of\,big\,drop,\,V = \frac{4}{3}\pi {R^3}\,\)                    \(...\left( {ii} \right)\)

Initial surface area of \(n\) droplets,

\({A_i} = n \times 4\pi {r^2} = \frac{{{R^3}}}{{{r^3}}} \times 4\pi {r^2}\)              \((Using (i))\)

\( = 4\pi \frac{{{R^3}}}{r} = \left( {\frac{4}{3}\pi {R^3}} \right)\frac{3}{r} = \frac{{3V}}{r}\)         \((Using (ii))\)

Final surface area of big drop

\({A_f} = 4\pi {R^2} = \left( {\frac{4}{3}\pi {R^3}} \right)\frac{3}{R} = \frac{{3V}}{R}\)                  \((Using (ii)\)

Decrease in surface area

\(\Delta A = {A_i} - {A_f} = \frac{{3V}}{r} - \frac{{3V}}{R} = 3V\left( {\frac{1}{r} - \frac{1}{R}} \right)\)

\(\therefore \,\,Energy\,released = surface\,tension\)

                                                     \( \times Decrease\,in\,surface\,area\)

\( = T \times \Delta A = 3VT\left( {\frac{1}{r} - \frac{1}{R}} \right)\)