explain why the value of g is zero at the centre of the earth
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There's gravity everywhere - it's an intrinsic property of all matter that has non-zero mass. If you were at the centre of the Earth it would feel like you were weightless. This is because all of the forces on you that result from the Earth's gravity are balanced. Mass attracts mass.
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acceleration due to earth's gravity at the centre of the earth is zero because at that point mass of the earth is equally distributed in all directions so pulling equal in all direction for net zero pull
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