Given,The mass of the particle be \\\\(m\\\\),Initilly it is on the centre of the earth, soThe work done in moving a particle from center of earth to its surface\\\\(\\ W=\\int_0^{R}Fdr\\\\)\\\\(=\\int_0^R(-\\dfrac{G(\\rho\\dfrac{4}{3}\\pi r^3)m}{r^2})dr\\\\)\\\\(=\\int_0^R(-\\dfrac{4G\\rho \\pi mr}{3})dr\\\\)\\\\(=\\dfrac{GMm}{2R},\\\\)we know that \\\\(F=\\dfrac{GMm}{R^2}=mg\\\\)\\\\(=\\dfrac{1}{2}mgR\\\\)(Since \\\\(g=\\dfrac{GM}{R^2}\\\\))So, The work done in shifting a particle of mass from the centre of the earth to the surface of the earth is \\\\(=\\dfrac{mgR}{2}.\\\\)