Question

why the value of g is 0 at the center of the earth

Answer 1

It is because it is the final position of earth magnetic source. The magnetic power or gravity origin from it

Answer 2

There is only zero gravity due to the earth itself. Obviously, an object cannot pull itself. That's why it is zero there. But gravity due to other objects still exists. For a more mathematical approach, you could consider the Earth to be a solid sphere( just an approximation, it isnt really one). Then using the formula for gravitational field due to solid sphere inside it, we see hat it will be zero.