Question

explain why the value of g is zero at the centre 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