Gravitational field

Refer the diagram below:

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At a distance r from the centre of the sphere, the gravity g is given by $g=\frac { Gm}{ { r }^{ 2 } }$ where m is the mass of uniform solid sphere of radius r, g is the gravity and G is the Gravitational Constant.

Now, $m=\frac { 4 }{ 3 } \pi r^{ 3 }\rho$ where $\rho$ is the density of the solid sphere. $\Rightarrow g=\frac { G\frac { 4 }{ 3 } \pi { r }^{ 3 }\rho }{ r^{ 2 } } \\ \quad \quad \quad =\quad G\frac { 4 }{ 3 } \pi { r }\rho$ When r=0, g = 0.

Hence, gravitational field at r=0 will be 0.