Question

Explain in mathematical way:
why the gravity at centre of earth is zero!?

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Answer 1

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.

Answer 2

Explanation:

Therefore, you would weigh more at the poles then at the equator, since the earth is not round, but flattened at the poles. ... 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!).