Physics - Gravitation Question with Solution | TestHub

Given, Escape velocity on the surface of earth, ${\mathrm{v}}_{\mathrm{e}}=11.1\mathrm{km}/\mathrm{h}$ i.e. $\begin{array}{rl}& {\mathrm{v}}_{\mathrm{e}}=\sqrt{2{\mathrm{gR}}_{\mathrm{e}}}\\ & {\mathrm{v}}_{\mathrm{e}}=\sqrt{\frac{2{\mathrm{GM}}_{\mathrm{e}}}{{\mathrm{R}}_{\mathrm{e}}}}\end{array}$ Mass of moon, $M_m=\frac{M_e}{81}$ Radius of moon, ${\mathrm{R}}_{\mathrm{m}}=\frac{{\mathrm{R}}_{\mathrm{e}}}{4}$ $\therefore$ Escape velocity on the surface of moon $\begin{array}{rl}& v_m=\sqrt{\frac{2G{M}_m}{R_m}}=\sqrt{\frac{2G\frac{Me}{81}}{\frac{R_e}{4}}}\\ & =\frac{2\sqrt{2}}{9}\sqrt{\frac{{\mathrm{GM}}_{\mathrm{c}}}{{\mathrm{R}}_{\mathrm{c}}}}=\frac{2}{9}\sqrt{\frac{2{\mathrm{GM}}_{\mathrm{c}}}{{\mathrm{R}}_{\mathrm{c}}}}=\frac{2}{9}{\mathrm{v}}_{\mathrm{e}}=\frac{2}{9}\times 11.1=2.46\mathrm{km}/\mathrm{h}\end{array}$