well, I'm sure the formula for finding the gravitational force is correct, if the radius is 0 the weight would ofcourse be undefined, then why is it 0 in all sources which I've read???
2007-09-18 06:04:46 · 2 answers · asked by Ice S 2 in Science & Mathematics ➔ Physics
The formula doesn't apply at the center of the earth. It assumes the mass of the earth is at the the center and you are at the surface or above. If you are under the surface of the earth, it is not applicable. The actual formula for gravity inside the earth is very much more complicated, because the mass of the earth is attracting you with different force in every direction.
However, If you were at the center of the earth the formula becomes simple because the mass of the earth would be distributed all around you and you would be attracted by its gravity in every direction equally. Therefore your weight would be zero.
2007-09-18 06:23:27 · answer #1 · answered by mr.perfesser 5 · 1⤊ 0⤋
Answer 1 is correct but the explanation is misleading. The formula for gravity inside the earth is very simple because the grav. accel inside a spherical shell of any thickness = 0 (see ref.). So in the force equation just substitute the current distance from the center (r1) for R, and the mass m1 of the sphere of radius r1 for M. For constant density, m1/M = r1^3/R^3. Then you have F = GM(r1^3/R^3)m/r1^2 and F is directly proportional to r1^3/r1^2 = r1. One interesting result of this is that in the "hole through the earth" scenario, an object dropped into the hole behaves as though it were attached to the center by a spring with k=gm/R.
2007-09-18 14:12:10 · answer #2 · answered by kirchwey 7 · 2⤊ 0⤋