(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that a hole has been drilled through the center of the Earth, and that an object is dropped into this hole. Write a first-order differential equation for the object's velocity,v as a function of the distance rfrom the Earth's center (i.e., an equation involvingdv/dr), and solve it to determine the speed the object achieves as it reaches the center of the Earth. Check this speed with the result you get from simple conservation of energy considerations. Consider the Earth's mass density to be uniform throughout. [Hint: recall Gauss' Law as it applies to the gravitational field of a spherically symmetric mass distribution.]

2. Relevant equations

I think the Gauss' Law for gravitation is simply to point out that the force is only effected by the mass enclosed, not the outer mass.

3. The attempt at a solution

Well, here is what I know...

The mass enclosed is a function of radius so [tex] a = \frac{dv}{dt} = \frac{Fm(r)}{r^2} [/tex]

I thought, to get [tex] \frac{dv}{dr} [/tex] I multiply both sides by [tex] \frac{dt}{dr} [/tex]. This gives me [tex] \frac {dt}{dr} \frac {Gm(r)}{r^2} = \frac {dv}{dr} [/tex]. Now I have a function in terms of dv/dr, but Im not sure if this is right or what to do next.

Thx for any tips or help!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Math Methods in Physics, find FODE

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