Question

why the value of g is zero at the centre of the earth

Answer 1

Here is the answer

Acceleration due to gravity on the Earth's surface is given as

g = GM/r^2

The value of g depends on the mass M of the earth and the radius R of the earth.
As we go deep inside the earth , our distance from the center of the earth decreases and no longer remains equal to the radius of the earth.(R).
Along with the distance, the part of the earth which contributes towards the gravitational force felt also decreases , decreasing the value of mass (M)

Due to the combined result of change in R and M , Value of g becomes zero at the center of the earth.

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