If acceleration due to gravity at the surface of the earth is g, the work done in slowly lifting a body of mass m from the earth's surface to a height R equal to the radius of the earth is : 

\(\frac{1}{2}mgR\)

The distance of the body from the center of the earth at a height R from the earth's surface = 2R.

The acceleration due to gravity at distance x from the center of the earth ( for x>R) = GM/x² 

Force on the body by the earth =mGM/x² 

Since the body is lifted slowly, hence the moving force is ≈ mGM/x² 

Hence the work done by the force in taking the body from R to 2R   = ∫m(GM/x²)dx  (limit of integration from R to 2R) 

  =mGM[-1/x] 

  =mGM[-1/2R+1/R] 

  =mGM/2R  =½m(GM/R²)R 

  = ½mgR