A body of mass m is situated at a distance 4R_e. above the earth's surface, where R_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 4R_e from the surface of earth

$\mathrm{U}=-\frac{{\mathrm{mgR}}_{\mathrm{e}}}{1+\mathrm{h}/{\mathrm{R}}_{\mathrm{e}}}=-\frac{{\mathrm{mgR}}_{\mathrm{e}}}{1+4}=-\frac{{\mathrm{mgR}}_{\mathrm{e}}}{5}$

[As h = 4R_e (given)]
So minimum energy required to escape the body will be $\frac{{\mathrm{mgR}}_{\mathrm{e}}}{5}$.