Question

Why is gravity 0 at the center of the earth ?

Answer 1

The further you go away from earth, lesser the gravitational force you experience. And closer you come to the surface of earth, more gravitational force acts on you. This is because of the inverse square law.

But as you keep on moving towards the center of the earth, the gravitational force acting, by the virtue of earth’s mass, on you will gradually abate and ultimately go zero once you reach the earth’s center. Not because there is no gravitational force down there but because at the center you will be completely surrounded or enveloped by earth, as a result you will be pulled by equal forces in all directions. Hence all the gravitational force lines will cancel out each other leaving you with zero net force.

Answer 2

Because all of the force on you that result from the earth's gravity is balanced. Mass attracts mass. There is the same amount of earthly mass in every direction. You would be pull equally in each direction and the net force on your body be zero But this doesn't mean that there is 0 gravity at the earth's centre.

In short, gravity is pulling pretty much equal in all directions that's why you'll feel zero gravity at the centre of the earth.