Physics - Fluid Question with Solution | TestHub

The work done is given as $\mathrm{W}=\mathrm{T}\Delta \mathrm{A}$ Volume of sphere is $\mathrm{V}=\frac{4}{3}\pi {\mathrm{r}}^3$ Area of sphere is $\mathrm{A}=4\pi {\mathrm{r}}^2$ $\therefore \mathrm{A}\propto {\mathrm{V}}^{\frac{2}{3}}$ $\therefore \mathrm{W}\propto {\mathrm{V}}^{\frac{2}{3}}$ $\frac{{\mathrm{W}}^{\prime }}{\mathrm{W}}=\frac{{\mathrm{V}}^{\frac{2}{3}}}{{\mathrm{V}}^{\frac{2}{3}}}$ $\frac{{\mathrm{W}}^{\prime }}{\mathrm{W}}=\frac{(2\mathrm{V}{)}^{\frac{2}{3}}}{{\mathrm{V}}^{\frac{2}{3}}}\dots .(\because \mathrm{V}=2\mathrm{V})$ $\therefore \frac{{\mathrm{W}}^{\prime }}{\mathrm{W}}=2^{\frac{2}{3}}=4^{\frac{1}{3}}$ $\therefore {\mathrm{W}}^{\prime }=4^{\frac{1}{3}}\mathrm{W}$