JEE Main 2026 — Center of Mass Momentum and Collision Question with Solution
JEE Main 2026 (22 January Shift 2)
Question
Given below are two statements :
Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
In the light of the above statements, choose the correct answer from the options given below :
Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
In the light of the above statements, choose the correct answer from the options given below :
Choose an option
Show full solutionCorrect option: D
Correct answer
DBoth Statement I and Statement II are true
Step-by-step explanation
Statement I: Total kinetic energy of a system equals . This is TRUE by definition.
Statement II: Total KE can be decomposed as , where the first term is kinetic energy of center of mass motion and the second is kinetic energy of particles relative to the center of mass. This is TRUE by the energy decomposition theorem (Koenig's theorem).
Both statements are true.
Statement II: Total KE can be decomposed as , where the first term is kinetic energy of center of mass motion and the second is kinetic energy of particles relative to the center of mass. This is TRUE by the energy decomposition theorem (Koenig's theorem).
Both statements are true.
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This is a previous-year question from JEE Main 2026, covering the Center of Mass Momentum and Collision chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.