Physics - Gravitation Question with Solution | TestHub

Energy required to escape the earth's gravitational field is $\frac{1}{2}{\mathrm{mV}}_e^2$ Energy given to the body is $=\frac{1}{2}\mathrm{m}{\left(3{\mathrm{V}}_{\mathrm{e}}\right)}^2$ $=\frac{9}{2}{\mathrm{mV}}_{\mathrm{e}}^2$ $\therefore$ If $\mathrm{V}$ is velocity of the body when it has escaped from earth's gravitational field then $$\begin{array}{rl}& \frac{1}{2}{\mathrm{mV}}^2=\frac{9}{2}{\mathrm{mV}}_{\mathrm{e}}^2-\frac{1}{2}{\mathrm{mV}}_{\mathrm{e}}^2\\ & \therefore \frac{1}{2}{\mathrm{mV}}^2=4{\mathrm{mV}}_{\mathrm{e}}^2\\ & \therefore {\mathrm{V}}^2=8{\mathrm{V}}_{\mathrm{e}}^2\\ & \mathrm{V}=2\sqrt{2}{\mathrm{V}}_{\mathrm{e}}\end{array}$$