Physics - Gravitation Question with Solution | TestHub

$\Rightarrow \frac{\mathrm{GMm}}{(\mathrm{R}+\mathrm{h}{)}^2}=\frac{{\mathrm{mv}}^2}{(\mathrm{R}+\mathrm{h})}$ $\Rightarrow \frac{\mathrm{GM}}{(\mathrm{R}+\mathrm{h})}={\mathrm{v}}^2$ ....(1) $\Rightarrow \mathrm{v}=(\mathrm{R}+\mathrm{h})\omega$ $\Rightarrow \mathrm{v}=(\mathrm{R}+\mathrm{h})\frac{2\pi }{\mathrm{T}}$ ....(2) $\Rightarrow \frac{\mathrm{GM}}{{\mathrm{R}}^2}=\mathrm{g}$ $\Rightarrow \mathrm{GM}={\mathrm{gR}}^2$ ....(3) Put value from (2) \& (3) in eq. (1) $\begin{array}{rl}& \Rightarrow \frac{{\mathrm{gR}}^2}{(\mathrm{R}+\mathrm{h})}=(\mathrm{R}+\mathrm{h}{)}^2{\left(\frac{2\pi }{\mathrm{T}}\right)}^2\\ & \Rightarrow \frac{{\mathrm{T}}^2{\mathrm{R}}^2\mathrm{g}}{(2\pi {)}^2}=(\mathrm{R}+\mathrm{h}{)}^3\\ & \Rightarrow {\left[\frac{{\mathrm{T}}^2{\mathrm{R}}^2\mathrm{g}}{(2\pi {)}^2}\right]}^{1/3}-\mathrm{R}=\mathrm{h}\end{array}$