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 the earth, R is the radius of the earth, and G is the gravitational constant)

Answer 1

Step 1: Given data:

$U_i$ = Self-potential energy of the earth

G = Universal gravitational consatnt

M = Mass of the earth

R = Radius of the earth

Step 2: Calculating the value of x

The self-potential energy of the earth is shown as follows.

$U_i=-\frac{3G{M}^2}{5R}$ ………(1)

But when all the mass above the earth is removed in infinity, its potential energy will be as follows.

$U_f=0$ ………(2)

So,

$E=U_f-U_i$

$E=0-\left(-\frac{-3G{M}^2}{5R}\right)$

$E=\frac{3G{M}^2}{5R}$ ………..(3)

As per the information given in the question.

$E=\frac{x}{5}\frac{G{M}^2}{5R}$ …….….(4)

When we get the equations (3) and (4) together.

$\frac{x}{5}\frac{G{M}^2}{R}=\frac{3G{M}^2}{5R}$

$X=3$

So here x is equal to 3.