A body of mass m is situated at a distance 4${\mathrm{R}}_{\mathrm{e}}$ above the earth's surface, where ${\mathrm{R}}_{\mathrm{e}}$ is the radius of earth. How much minimum energy be given to the body so that it may escape

Potential energy of the body at a distance 4${\mathrm{R}}_{\mathrm{e}}$ from the surface of earth

   U = $-\frac{GMm}{R_e+h} = -\frac{mg{R_e}^2}{R_e+4R_e} = -\frac{{{\mathrm{mgR}}^2}_{\mathrm{e}}}{5R_e}=-\frac{mg{R}_e}{5}$

[As h = 4${\mathrm{R}}_{\mathrm{e}}\left(\mathrm{given}\right)$]

So minimum energy required to escape the body will be $\frac{{\mathrm{mgR}}_{\mathrm{e}}}{5}$