Down in a cave below the surface of the earth there is:
a) more gravity than at the earth's surface
b) less gravity than at the earth's surface
c) the same gravity as at the surface
Assume the earth's density is the same all the way through. Of course it isn't. But simplistic idealized situations must be thoroughly understood before details can be appreciated.
2007-11-19 16:20:39 · 6 answers · asked by ? 6 in Science & Mathematics ➔ Physics
Under the problem's scenario, if we are talking about the accleration of gravity, the shell theorem, which has been bantered about during the last three episodes of this series by several of your intrepid answerers applies. This theorem which was the answer to Newton's enigma states that with a sphere, you can ignore the contribution from mass located farther from the center of gravity than the observer in determining the local acceleration of gravity. This means that the accleration of gravity in a cave would be less than on the earth's surface. (Answer B)
But since the problem specifies gravity, not the acceleration of gravity. There is more gravity in a cave because you are dropping farther down into the gravity well caused by earth's mass. The man in the cave's watch will run slower. Time will dialate compared to the surface which ergo proves the increased gravity field. In other words, according to Einstein and general relativity, the answer is (a) there is "more gravity than at the earth's surface"
But then again, my recollection is that because the earth's core is so much denser than the crust, the acceleration of gravity actually increases as you dig deeper. Basically because the increasing "1/r" component more than offsets the decreasing "m" component in Newton's law of Universal Gravitation. I think I'll have to check that tomorrow after coffee................
2007-11-19 16:48:17 · answer #1 · answered by Frst Grade Rocks! Ω 7 · 4⤊ 0⤋
b) less gravity than at the earth's surface.
At a distance x below the surface of earth value of acceleration due to gravity g(x) is
g(x) = g * [(R - x) / R] where,
g = acceleration due to gravity on the surface of the earth = 9.8 m/s^2,
R = radius of the earth.
2007-11-20 01:01:03 · answer #2 · answered by Madhukar 7 · 3⤊ 0⤋
You're really trying to strain my brain aren't you!
I would say B is correct. Closer to the middle I'm effected by less mass, hence less gravity.
Not only that, there's a 33.3 chance I have the best answer! :)
2007-11-20 00:45:18 · answer #3 · answered by Pragmatism Please 7 · 2⤊ 1⤋
A.
I know that going miles into the atmosphere, gravity's effect is less and less, so why wouldn't the inverse be true? =)
2007-11-20 00:48:22 · answer #4 · answered by Anonymous · 1⤊ 1⤋
B
And I'm not going to argue about it.
B!
2007-11-20 00:48:58 · answer #5 · answered by Paa Pop! 2 · 2⤊ 2⤋
A.
No B.
I mean A.
B?
Wait it's C isn't it!
C C C C C!
2007-11-20 00:42:19 · answer #6 · answered by I want my two dollars? 3 · 3⤊ 1⤋