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Say you drill a hole all the way through the Earth, and drop a rock in...

Say you drill a hole all the way through the Earth, and drop a rock in the hole. It will fall in, then continue "up" the hole once it gets past the center of the Earth, then come to a stop at the other end of the hole, and fall back in, eventually coming back to you (assuming no friction, of course). (a) You can use Gauss' Law to find the force of gravity as a function of distance from the center of the Earth. It's a lot like the spherical charge distribution problem from Phys2015: only the mass inside the Gaussian surface matters. Make your life easier by assuming a uniform density Earth. (b) Show that the oscillation is really just SHM, and find its period: how long do you have to wait to get your rock back?

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