Physics - Fluid Question with Solution | TestHub

Total surface energy before coalesce $$E_1=2\left(4\pi R^2\right)T$$ But $\frac{4}{3}\pi {\mathrm{R}}^3\times 2=\frac{4}{3}\pi {\mathrm{R}}^{13}$ $$R^{\prime }=(2{)}^{1/3}R$$ Total surface energy after coalescing $$\begin{array}{rl}& {\mathrm{E}}_2=4\pi R^{\prime 2}\mathrm{T}=4\pi (2{)}^{2/3}{R}^2\mathrm{T}\\ & \frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}=\frac{2\left(4\pi R^2\right)\mathrm{T}}{4\pi (2{)}^{2/3}{\mathrm{R}}^2\mathrm{T}}=2^{1-\frac{2}{3}}=2^{1/3}\end{array}$$