Physics - Gravitation Question with Solution | TestHub

Minimum value of kinetic energy required to escape from the gravitational influence of the earth is given by ${\mathrm{k}}_{\mathrm{e}}=\frac{\mathrm{GMm}}{\mathrm{R}}$ $\therefore$ The kinetic energy of projection is $\mathrm{K}=\frac{\mathrm{GMm}}{2\mathrm{R}}$ At the highest point the kinetic energy become zero. Loss of kinetic energy $=$ Gain in potential energy $\begin{array}{rl}& \frac{\mathrm{GMm}}{2\mathrm{R}}=\frac{\mathrm{GMm}}{\mathrm{R}}-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}\\ \therefore & \frac{1}{2\mathrm{R}}=\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{R}+\mathrm{h}}\\ \therefore & \frac{1}{\mathrm{R}+\mathrm{h}}=\frac{1}{\mathrm{R}}-\frac{1}{2\mathrm{R}}=\frac{1}{2\mathrm{R}}\\ \therefore & \mathrm{R}+\mathrm{h}=2\mathrm{R}\\ \therefore & \mathrm{h}=2\mathrm{R}-\mathrm{R}=\mathrm{R}\end{array}$