Question

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5}\frac{G{M}^2}{R}$
where $x$ is
(Round off to the Nearest Integer)
($M$ is the mass of earth, $R$ is the radius of earth, $G$ is the gravitational constant)

Answer 1

Self potential energy of the earth is given as, $U_i=-\frac{3}{5}\frac{G{M}^2}{R}$
When all the mass of the earth is removed to infinity, its potential energy will be, $U_f=0$

Energy given, $E=U_f-U_i$
$E=0-\left(\frac{3}{5}\frac{G{M}^2}{R}\right)=\frac{3}{5}\frac{G{M}^2}{R}$
So, $x=3$