Physics - Gravitation Question with Solution | TestHub

(D) Energy required to raise the satellite to a height $h$ from surface of earth is given by $\begin{array}{rl}U& =-\frac{GMm}{(R+h)}-\left(-\frac{GMm}{R}\right)\\ & =\frac{GMm}{R}-\frac{GMm}{(R+h)}=GMm\left[\frac{1}{R}-\frac{1}{R+h}\right]\\ & =GMm\left[\frac{R+h-R}{R(R+h)}\right]=GMm\frac{h}{R(R+h)}\end{array}$ KE of the satellite is given by $\begin{array}{rl}\mathrm{K}& =\frac{1}{2}{\mathrm{mV}}_0^2=\frac{1}{2}\mathrm{m}\frac{\mathrm{GM}}{(\mathrm{R}+\mathrm{h})}\\ \therefore \frac{\mathrm{U}}{\mathrm{K}}& =\frac{\mathrm{GMmh}}{\mathrm{R}(\mathrm{R}+\mathrm{h})}\times \frac{(\mathrm{R}+\mathrm{h})2}{\mathrm{mGM}}=\frac{2\mathrm{h}}{\mathrm{R}}\end{array}$