Physics - Fluid Question with Solution | TestHub

Volume of $\mathrm{n}$ smaller droplets $=$ Volume of bigger drop $\begin{array}{rl}& \mathrm{n}\frac{4}{3}\pi {\mathrm{r}}^3=\frac{4}{3}\pi {\mathrm{R}}^3\\ & \therefore \mathrm{R}={\mathrm{n}}^{\frac{1}{3}}\cdot \mathrm{r}\\ & \mathrm{r}=\frac{\mathrm{R}}{{\mathrm{n}}^{\frac{1}{3}}}\end{array}$ $\begin{array}{rl}\text{ Work done }W& =\left[n\cdot 4\pi r^2-4\pi R^2\right]T\\ & =4\pi \left[n\cdot \frac{R^2}{n^{\frac{2}{3}}}-R^2\right]T\\ & =4\pi R^2\left[n^{\frac{1}{3}}-1\right]T\end{array}$