Question

Why the gravitational force is zero at the centre of earth? Explain Mathematically.
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Answer 1

So that even if we're closer to the center of mass of the earth, gravity will not go up much. If you are at the center of the earth, gravity is zero because all the mass around you is pulling "up" (every direction there is up!).

Answer 2

Answer:

At the centre of Earth, the force due to upper half of the Earth will cancel the force due to lower half. In the similar manner, force due to any portion of the Earth at the centre will be cancelled due to the portion opposite to it. Thus, the gravitational force at the centre on any body will be 0.

Explanation:

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