explain why the value of g is zero at the centre of the earth.
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Yes. 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. There is the same amount of earthly mass in every direction. So you would be pulled equally in each direction and the net force on your body would be zero. This does not mean that there is no gravity at the Earth's centre. There's an awful lot of gravity there!
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because it has no surface area
revengerdon:
Then what is the relation between surface area and gravity
As the distance from the centre decreases, the acceleration due to gravity also decreases.
At the centre the distance is zero, hence gravity is zero.
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