A ring of matter is a familiar structure in planetary and stellar astronomy. Examples include Saturn€™s rings and a ring nebula. Consider a uniform ring of mass 2.36 X 1020 kg and radius 1.00 X 108 m. An object of mass 1 000 kg is placed at a point A on the axis of the ring, 2.00 X 108m from the center of the ring (Figure P13.53). When the object is released, the attraction of the ring makes the object move along the axis toward the center of the ring (point B). (a) Calculate the gravitational potential energy of the object€“ring system when the object is at A. (b) Calculate the gravitational potential energy of the system when the object is at B. (c) Calculate the speed of the object as it passes through B.

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Figure P13.53