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 \(\frac x5 \frac{GM^2}R\) 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

Answer is 3

Energy given = U_f – U_i

Comments

How is Ui equal to 3GMsq/5R

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Density will be same after break up.
1st break up will be in the form of hemisphere.
ρ_E = ρ_H
M/(4πR^2+πR^2)dR = m/(2πR^2+πR^2)dR
m = (3πR^2dR)/(5πR^2dR) M
= 3/5 M