Explain why the value of the g is zero at the center of the earth
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The value of g is zero at the centre of earth because at that point the mass of the earth is equally distributed in all directions, so the pulling is equally in all directions for a net zero pull
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At the centre of Earth, the force due to upper half of the Earth will cancel the force due to lower half. Therefore, when F=0, then g has to be 0. Thus, the value of g is zero at centre of the Earth.
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