Physics - Gravitation Question with Solution | TestHub

$\begin{array}{rl}\text{ The kinetic energy given to the body }=\mathrm{k}& =\frac{1}{2}\mathrm{m}(2\mathrm{Ve}{)}^2\\ & =\frac{1}{2}\left(4{\mathrm{mV}}_{\mathrm{o}}^2\right)\end{array}$ The kinetic energy required to escape from the earth's gravitational field $={\mathbf{K}}^{\prime }=\frac{1}{2}{\mathbf{mV}}_0^2$ If its velocity is $\mathrm{V}$ after escaping from the earth's gravitational field then its kinetic energy will be $$\begin{array}{rl}\frac{1}{2}{\mathrm{mV}}^2& =\frac{1}{2}\left(4{\mathrm{mV}}_{\mathrm{e}}^2\right)-\frac{1}{2}{\mathrm{mV}}_{\mathrm{e}}^2\\ & =\frac{1}{2}\left(3{\mathrm{mV}}_{\mathrm{e}}^2\right)\\ \therefore {\mathrm{V}}^2& =3{\mathrm{V}}_{\mathrm{e}}^2\\ \therefore \mathrm{V}& =\sqrt{3}{\mathrm{V}}_{\mathrm{e}}\end{array}$$