Question

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

Answer 1

Here is your answer

g means acceleration due to gravity

Let the mass of earth be M and a body placed at its surface be m and the gravitational force between them be F. Distance between the object and centre of earth be r

so, by Universal law of gravitation
F= GMm/ r^2 where G is gravitational constant
F= GMm/r^2 ----(i)
since mass of object is negligible in respect to the mass of earth
so, it is taken as 0

F= GM×0/r^2 [from (i)]
mg=0 [by Newton's 2nd law of motion F=ma, where a=g]

g=0/m
g=0
So value of g at the surface of earth is zero

Hope it is useful

Answer 2

The value of g [acceleration due to gravity] is 0 m/s² at the center of the earth as in the center of the earth the distance between the center of the earth and the object becomes 0 meters and it's square will also be 0. And when we divide the product of mass and G with 0 it will be undefined and we take this as 0.

So, the value of g at the center of the earth is 0 m/s².