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  4. A body of mass m is situated at a distance 4Re above the earth’s surface, where Re is the radius of earth. How much minimum energy be given to the body so that it may escape

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Q. 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

Gravitation

Solution:

Potential energy of the body at a distance $4R_e$ from the surface of earth
$U = -\frac{mgR_{e}}{1+hR_{e}} = - \frac{mgR_{e}}{1+4} = -\frac{mgR_{e}}{5}$
[As $h = 4R_{e}$ (given)]
So minimum energy required to escape the body will be $\frac{mgR_e}{5}$.