Question

why value of g is zero at center of the earth

Answer 1

Because if you consider earth as a point mass, ALL the Centre of mass will be concentrated at the centre most point.

For a point, we say will be g = 0 there.

Answer 2

It isn't 0 the value of g is not defined at the centre of the earth.
Reason,
g=Gm/r²
Since,
r is the distance between the object and the centre of the earth.
Since,
The object is at the centre.
Therefore,
The value of r will be 0
Now,
g=Gm/0=Not defined

Hope this helps you!