A certain number of spherical drops of a liquid of radius $$r$$ coalesce to form a single drop of radius $$R$$ and volume $$V.$$ If $$T$$ is the surface tension of the liquid, then

Solution :
$$\eqalign{ & {\text{As energy released}} = \left( {{A_f} - {A_i}} \right)T \cr & {\text{where,}}\,{A_i} = 4\pi {R^2} = \frac{3}{R} \times \left( {\frac{{4\pi }}{3} \times {R^3}} \right) = \frac{{3V}}{R} \cr & {\text{and}}\,{A_f} = 4\pi {r^2} = \frac{V}{{\frac{4}{3}\pi {r^2}}}4\pi {r^2} = \frac{{3V}}{r} \cr & \therefore {\text{Energy released}} = 3VT\left[ {\frac{1}{r} - \frac{1}{R}} \right] \cr} $$