the value of gravitational acceleration below the surface of earth at a distance r from the center of the earth
= G *(mass of earth exerting gravitational force*)/distance2
= G ( 4/3 * π*r3)ρ /r2 = 4/3*π*G*r*ρ
4/3*π*G*(R-d) .....(A)
where G = gravitational constant
r= distance from the center of the earth
ρ= density of the earth
d = depth below the surface
R= radius of earth
the value of gravitational acceleration above the surface of earth at a height h from the center of the earth
= G ( 4/3 * π*R3)ρ/(R+h)2 ...............(B)
equation A = equation of B for value of acceleration of gravity to be equal
4/3*π*G*(R-d)*ρ =G ( 4/3 * π*R3)ρ/(R+h)2
(R-d) (R+h)2=R3
using radius of earth = 6371 km ( assumed not provided in the question )
height h = 64 km
and solving above equation we get d= depth = 126.09 km
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