Value of g at the centre of the earth:

If g is the gravitational acceleration at the earth’s surface and g’ is the gravitational acceleration at a depth \( h \) from the surface of earth.

then we know that, \( g’=g\left(1-\frac{h}{R}\right) \). Where R is the radius of the earth. Read In Detail.

Now at the centre of the earth \( h=R \), so the gravitational acceleration at the centre of the earth is

\( g’= g\left(1-\frac{R}{R}\right) = 0 \).