Question

Explain why the value of g is zero at the centre of the Earth

Answer 1

There's gravity everywhere - it's an intrinsic property of all matter that has non-zero mass. If you were at the centre of the Earth it would feel like you were weightless. This is because all of the forces on you that result from the Earth's gravity are balanced. Mass attracts mass.

Answer 2

The actual yet conceptual answer for this is because when considering the centre most particle of the center of the earth, the gravity will be 0 because it is the particle which holds the power of gravity for the other particle towards outside. I hope you can understand.