Answer: Assume that the earth is a solid sphere of uniform density with mass and radius

Chapter 17, Problem 21

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Assume that the earth is a solid sphere of uniform density with mass and radius mi. For a particle of mass within the earth at a distance from the earths center, the gravi tational force attracting the particle to the center is where is the gravitational constant and is the mass of the earth within the sphere of radius .(a) Show that .(b) Suppose a hole is drilled through the earth along a diameter.Show that if a particle of mass is dropped from restat the surface, into the hole, then the distance ofthe particle from the center of the earth at time is given bywhere .(c) Conclude from part (b) that the particle undergoes simpleharmonic motion. Find the period T.(d) With what speed does the particle pass through the centerof the earth?