The value of g at depth $x$ from the surface of the earth is given by, \[g’=\left(1-\frac{x}{R}\right)g\]

[Variation of g due to the depth from the surface of the earth]

At the centre of the earth, $x=R.$ So,

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

Hence, the value of $g$ is zero at the centre of the earth.