Question

If mass of earth decreases by 25 and its radius by 50+ then acceleration due to gravity at its surface decreases by nearly 1) 89+ 2)67+ 3)33+ 4)11+
How Explain the concept + logic.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2} \\ \mathrm{Mass}\mathrm{of}\mathrm{earth}\mathrm{decrease}\mathrm{by}25\%,\mathrm{remaining}=75\%\mathrm{of}\mathrm{M}=\frac{75}{100}\mathrm{M} \\ \mathrm{radius}\mathrm{of}\mathrm{earth}\mathrm{increase}\mathrm{by}50\%,\mathrm{new}\mathrm{radius}=150\%\mathrm{of}\mathrm{R}=\frac{150}{100}\mathrm{R} \\ \mathrm{g}\text{'}=\frac{\mathrm{G}\left({\displaystyle \frac{75}{100}}\mathrm{M}\right)}{{\left({\displaystyle \frac{150\mathrm{R}}{100}}\right)}^2} \\ \mathrm{g}\text{'}=\mathrm{G}\frac{\mathrm{M}}{{\mathrm{R}}^2}\left[\frac{75}{100}\times \frac{10000}{150\times 150}\right] \\ \mathrm{g}\text{'}=\mathrm{g}\frac{5}{15} \\ \mathrm{g}\text{'}=0.33\mathrm{g} \\ \mathrm{Acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity}\mathrm{decreases}\mathrm{by}=\mathrm{g}-0.33\mathrm{g}=0.67\mathrm{g} \\ \mathrm{Acceleration}\mathrm{due}\mathrm{to}\mathrm{gravity}\mathrm{decreases}\mathrm{by}=0.67\times 100\%=67\% \end{gathered}$$