Question

A body of mass $m$ is situated at 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

• A. $mg{R}_e$
• B. $2mg{R}_e$
• C. $\frac{mg{R}_e}{5}$
• D. $\frac{mg{R}_e}{16}$

Answer 1

The correct option is C $\frac{mg{R}_e}{5}$

Potential energy of the body at a distance 4$R_e$ from the surface of earth

$U=-\frac{mg{R}_e}{1+n/R_e}$

$=-\frac{mg{R}_e}{1+4}=-\frac{mg{R}_e}{5}$ As $h=4R_e$

So, minimum energy required to escape the body will be $\frac{mg{R}_e}{5}$