What is the value of g(acceleration due to gravity) at the center of earth?
It is zero – you have to use Gauss’s Law/Theroem to show this. Spherically symmetric mass distribution Main article: Shell theorem In the case of a spherically symmetric mass distribution we can conclude (by using a spherical Gaussian surface) that the field strength at a distance r from the center is inward with a magnitude of G/r² times only the total mass within a smaller distance than r. All the mass at a greater distance than r from the center can be ignored. For example, a hollow sphere does not produce any net gravity inside. The gravitational field inside is the same as if the hollow sphere were not there (i.e. the resultant field is that of any masses inside and outside the sphere only). Although this follows in one or two lines of algebra from Gauss’ law for gravity, it took Isaac Newton several pages of cumbersome calculus to derive it directly using his law of gravity; see the article Shell theorem for this direct derivation.
