3. 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 10* m. An object of mass 1 000 kg is placed at a point A on the axis of the ring, 2.00 x 10* m from the center of the ring. 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) Find the gravitational potential energy of the object-ring system when the object is at A. Do the integral first to find an expression and then calculate the numerical value. (b) Determine 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.

3. 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 10* m. An object of mass 1 000 kg is placed at a point A on the axis of the ring, 2.00 x 10* m from the center of the ring. 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) Find the gravitational potential energy of the object-ring system when the object is at A. Do the integral first to find an expression and then calculate the numerical value. (b) Determine 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.