Why gravitational force at the center og earth is zero

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Why value of 'g' is zero at center of Earth?

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When we move towards centre of earth, the mass is equally distributed in all directions.

The mass beneath you = Mass in front of you = Mass behind you

Thus, all the gravitational forces applied cancel each other and acceleration due to gravity (g) at centre of earth on centre of earth becomes zero (0).

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The general equation of acceleration due to gravity is;-

g =

Assuming earth to be a perfect sphere and considering its uniform density.

We make the following adjustments in the following equation.

g =

Multiplying and dividing RHS by volume 'V'.

g =

We know that;-

= Density, ρ

Therefore,

g =

For sphere;-

V = π

This makes

g = π ×

g =

So, at center of Earth

since, r = 0

so, g = 0.

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