Posted by jim on Tuesday, March 6, 2012 at 6:13pm.
The value of g at Earthâ€™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?

physics  drwls, Tuesday, March 6, 2012 at 7:16pm
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
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