Question

How much below the surface of the earth does the acceleration due to gravity becomes 99% of its value at surface?

Answer 1

Let the depth at which acceleration due to gravity ( g) becomes 70% or 7g/10 = d. 

We know that 

gd = g (1-d/r)

Given

gd= 7g/10

Also, R = 6400 km [ Radius of earth ] 

7g/10 = g [ 1 - d / 6400] 

7/10= 1-d/6400

d/6400 = 1 - 7/10

d/6400 = 3/10 

d = 3 x 6400/10

d= 1920 km. 

Therefore, 
1920 km

below the surface of the earth does the acceleration due to gravity become 99% of its value at the surface of the earth.