Answer: Assume that the earth is a solid sphere of uniform

Chapter 17, Problem 17.314

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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 gravitational 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 rest at the surface, into the hole, then the distance of the particle from the center of the earth at time is given by where . (c) Conclude from part (b) that the particle undergoes simple harmonic motion. Find the period T. (d) With what speed does the particle pass through the center of the earth?