Question

A very narrow hole is drilled all the way through the Earth(through its center) and evacuated (i.e. there is neither airresistance nor friction). A small object of mass m is dropped intothe hole at the surface.

a) Describe its motion qualitatively. The Earth has radius 6375 km.Assume that the Earth has uniform density, and state any otherassumption you choose to make. (Hint: The answer must make physicalsense).

b) Does the force an object an object experiences near the surfaceof the Earth need to be continuous as it passes from above tobeneath the surface?

c) Does the gravitational potential energy an object experiencesnear the surface of the Earth need to be continuous as it passesfrom above to beneath the surface?

d) What is the force on the object for points within the tube (r< RE)? (Express the answer with a constant, C, and a power, n,of the radial distance from the center, r, i.e. F = Crn).

e) How long does it take to return to its startingpoint?

f) What is the gravitational potential energy for pointswithin the Earth (r < RE)?

g) What is the gravitational potential energy at the center ofthe Earth?

h) What is the speed of the mass at the center of theEarth?

Thank you in advance for any help on how to solve thisproblem!