The gravitational force of attraction acting on an object of mass m is given by `F = (m*g*r)/R_e` where r is the distance of the object from the center of the Earth and `R_e` is the radius of the Earth.
The work required to bring an object with mass 1 kg from the center of the Earth to the surface is given by :
`int_0^(R_e) m*g*r/R_e dr`
= `(m*g/R_e)*(1/2)*(R_e^2 - 0)`
The value of g is 9.8 m/s^2 and `R_e` = 6371 km. Using these in the formula derived for the work done gives (1*9.8*6371*10^3)/2 = 31.217*10^6 J
The work done to bring an object with mass 1 kg from the center of the Earth to the surface is approximately 31.217*10^6 J