(a) Show that if a particle describes a circular orbit under the influence of an attractiv...

(a) Show that if a particle describes a circular orbit under the influence of an attractive central force directed toward a point on the circle, then the force varies as the inverse-fifth power of the distance.

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(b) Show that for the orbit described the total energy of the particle is zero.

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(c) Find the period of the motion.

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(d) Find , and v as a function of angle around the circle and show that all three quantities are infinite as the particle goes through the center of force.