Why g is zero at the cetre of the earth?

At the center, for every particle of mass in the earth toward which you're gravitationally

attracted, there's an equal particle with the same mass, located at the same distance

from you in exactly the opposite direction, balancing out the force toward the first one.

That statement assumes that the earth is a perfect sphere with the same distribution

of mass in every direction from the center. The real earth is oddly shaped, lumpy and

bumpy, so the acceleration of gravity wouldn't be exactly zero at the center.