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(b) For the products the coordinates can be the C-D and A-B distances and the distance from the center of mass of AB to the center of mass of CD....
(b) For the products the coordinates can be the C-D and A-B distances and the distance from the center of mass of AB to the center of mass of CD. Express the kinetic energy in these coordinates. (c) You can then examine the kinetic energy of C-D motion and show that it is uncoupled to the other motions and is unaffected by the rearrangement. Where is the approximation?