Physics - Gravitation Question with Solution | TestHub

If$g$and$g_h$denote the acceleration due to gravity at the Earth's surface and at the height$h$above the Earth's surface respectively, then

$\frac{g_h}{g}=\frac{R^2}{{(R+h)}^2}$

But according to the equation

$g_h=g-\frac{20}{100}g=\frac{80}{100}g=\frac{4}{5}g$

$\therefore \frac{4}{5}=\frac{R^2}{{\left(R+h\right)}^2}\mathrm{o}\mathrm{r}\sqrt{\frac{4}{5}}=\frac{R}{\left(R+h\right)}$

or$\frac{2}{\sqrt{5}}=\frac{R}{R+h}\mathrm{o}\mathrm{r}2R+2h=\sqrt{5}R$

or$2h=\left(\sqrt{5}-2\right)R\mathrm{o}\mathrm{r}h=\frac{\left(\sqrt{5}-2\right)R}{2}=\left(\frac{\sqrt{5}}{2}-1\right)R$