Question

why does acceleration due to gravity become zero at earth core

Answer 1

the variation of acceleration due to gravity with depth is given as

g' = g.[1 - d/R]

now, at the center of the earth, d = R [the distance is measured from earth's surface where d = R]

so,

g' = g.[1 - R/R] = g.[1-1]

thus,

as the earth's center the acceleration due to gravity will be

g' = 0