There is no mass at exact center of Earth to provide a gravitational pull and thus a gravitational acceleration⇒acceleration due to gravity GM/r2 is 0 at center
According to shell theorem-no outside mass provides gravitational pull at center of Earth.Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has both magnitude and direction, hence, it’s a vector quantity.
According to the universal law of gravitation , f = GmM/(r+h)2
Where,
f = force between two bodies,
G = universal gravitational constant (6.67×10-11 Nm2/kg2)
m = mass of the object,
M = mass of the earth,
r = radius of the earth.
h = height at which the body is from the surface of the earth.
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Physics