Why at the centre of earth gravitational force is zero .is it because r=0 or the mass of earth at that point is zero?
Acceleration due to the earth's gravity is zero at the centre of the Earth because at that point the mass of the earth is equally distributed in all directions, so pulling equally in all directions for a net zero pull.
g′=g(1−hR)
wherehisthedistancefromthesurfaceoftheearthinside,towardsthecenter.
As the distance from the centre decreases, the acceleration due to gravity also decreases.
At the centre the distance is zero, hence gravity is zero.
Why is the there no g-force in the center of the Earth? Because at the center, the mass above you the the same as the mass beneath you; the mass in front of your the the same as the mass behind you, and so on. Therefore, all the gravitational forces cancel out each other. Therefore, the gravitational acceleration at the ideal center of the Earth is 0.