Question

why there is no gravity at centre of earth?

Answer 1

At Earth's center, as g = 0 and the center of gravity would not exist also for any body.

There is a direct relation between acceleration due to gravity and force experienced by an object on the earth[Universal Gravitational force] and it states that the force maximum on the surface of earth and it decreases on going above the surface of earth or on going inside the surface of the earth and ultimately becomes Zero at the centre.