Question

Why the value of g is zero at the centreof earth?

Answer 1

Near the surface of the Earth (sea level), gravity decreases with height such that linear extrapolation would give zero gravity at a height of one half of the earth's radius - (9.8 m.

Answer 2

first of all gravity is all about mass. now at the centre the mass which is above u is same as it is beneath u it is same in front of u and same on the back side. so actually all these just cancel out each other hence the gravity become zero.