Question

The weight of an object on earth is 392N. what will be the weight of this body on a planet whose weight is double that of earth and radius is 4 times than that of earth??

Answer 1

$$\begin{gathered} \frac{\mathrm{W}\text{'}}{\mathrm{W}}=\frac{\mathrm{mg}\text{'}}{\mathrm{mg}} \\ \frac{\mathrm{W}\text{'}}{\mathrm{W}}=\frac{\mathrm{g}\text{'}}{\mathrm{g}} \\ \mathrm{But},\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2} \\ \mathrm{Hence}, \\ \mathrm{W}\text{'}=\mathrm{W}\times \frac{\mathrm{M}\text{'}}{\mathrm{M}}\times {\left[\frac{\mathrm{R}}{\mathrm{R}\text{'}}\right]}^2 \\ =392\times 2\times {\left[\frac{1}{4}\right]}^2 \\ =49\mathrm{N} \end{gathered}$$