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Imagine you have drilled a narrow borehole through the center of the Earth, all the way...

Imagine you have drilled a narrow borehole through the center of the Earth, all the way to the other side. If you step into the hole and fall straight down, what will your velocity be when you reach the center of the Earth?

The radius of the Earth is 6356 km, and the mass of the Earth is 5.972x1024 kg. The value of Newton’s gravitational Constant is G= 6.67×10−11 N⋅m2/kg2. Ignore any effects from air resistance, or the rotation of the Earth. You may assume the Earth has a uniform density. Hint: Remember the shell theorem. The force you experience as you fall will NOT be constant.

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Answer #1

Use the equation for potential at the surface and the centre of the earth to find the change in potential and use that with work energy theorem to find the final speed as shown below

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