How much below the surface of the earth does the acceleration due to gravity become 1percent of its value at the earth surface? The earth is assume to be a sphere of radius 6.4×10^6m.

Answer 1

Beneath the surface, gravity is basically a linear function of the radius. So, at 1/100 the radius, g is reduced by a factor of 1/100

See the discussion here:

http://physics.stackexchange.com/questions/99117/why-gravity-decreases-as-we-go-down-into-the-earth