The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity:
1.
will be directed towards the centre but not the same everywhere.
2.
will have the same value everywhere but not directed towards the centre.
3.
will be the same everywhere in magnitude directed towards the centre.
4.
cannot be zero at any point.
Hint: The acceleration due to gravity depends on mass distribution of the Earth.
If we assume the earth as a sphere of uniform density, then it can be treated as a point mass placed at its centre. In this case acceleration due to gravity g = 0, at the centre. It is not so if the earth is considered as a sphere of non-uniform density, in that case, the value of g will be different at different points and cannot be zero at any point.
