Suppose that a hole has been drilled through the center of the Earth, and that a

Question

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 r from the Earth's center (i.e., an equation involving dv=dr), and solve it to determine the speed that 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'

Explanation / Answer

So... a=dvdt=Gm(r)r2=4/3G?pr ... there doesnt seem to be any variable to separate, is there? I can move the dt over to the right hand side.. dv=4/3G?prdt and integrate both sides to get... v=4/3F?prt+C

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