The value of acceleration due to gravity ′g′, at earth's surface is 10m/s2. Its value at the centre of the earth which is assumed to be sphere of radius ′R′ and uniform mass density, is

 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.