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Two particles coIIide elastically. In the laboratory frame one of the particles is originally at rest. (a) In which frame is the total kinetic energy least? (A) The laboratory frame (B) The center-of-mass frame (C) The kinetic energy is the same in the laboratory frame and the center-of-mass frame. (D) The question cannot be answered without more information, (b) In which frame is the magnitude of the total momentum least? (A) The laboratory frame (B) The center-of-mass frame (C) The momentum is the same in the laboratory frame and the center-of-mass frame. (D) The question cannot be answered without more information.
(a) The correct option is (D) the question cannot be answered without more information.Kinetic energy is the energy possessed by a body by virtue of its motion. Kinetic energy of the particle is depending on the reference point of observation. If both the particles have same velocity , then total kinetic energy by of the system can fully removable by choosing suitable inertial frame of reference. Here you cannot find the total kinetic energy which is least in the reference frame due to the lack of information. Thus the question cannot be answered without more information. Thus option (D) is correct.(a) The correct option is (B) the center-of-mass frame.In center of mass frame, the total momentum of the system is equal to zero. Thus the magnitude of the total momentum is least at the center of mass frame. Therefore option (B) is correct.
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