The value of g at Earth’s surface is about 9.8 m/s^2. If Earth were of uniform density (same mass/volume throughout), what would the value of g be inside Earth at half its radius?

Answer 1

g'(r) = G* m(r)/r^2, where m is the mass within radius r.
G is the universal constant of gravity

At r = R/2, 1/8 of the earth's total mass is inside. Call the value of g there g'.
g'(at r = R/2) = G*(M/8)/(R/2)^2
= (1/2)G*M/R^2

= g/2 = 4.9 m/s^2