n the approximation that the Earth is a sphere of uniform density, it can be shown that the gravitational force it exerts on a mass m inside the Earth at a distance r from the center is mg(r/R), where R is the radius of the Earth. (Note that at the the surface and at the center, the force reduces to what we would expect.) Suppose that there were a hole drilled along a diameter straight through the Earth, and the air were pumped out of the hole. If an object is released from one end of the hole, find an expression for how long it will take to reach the other side of the Earth.
I don't really know what to do.
I know you can use to potential and kinetic energy equations to find velocity which would help find the period since T = 2*R/V (if V*T=2R)
But, I keep getting the answer wrong, solving it that way. It might be my use of the energy equations. I understand that PE is supposed to be highest at the surface and 0 at the center, since Fofg would be 0 because r from center would be 0. But where do I Go from there?
Do I use the F of gravity inside earth equation given for g in PE equation m*g*h?
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