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JEE Main202622 January 2026Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

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 corre

Options

  1. AStatement I is true but Statement II is false
  2. BBoth Statement I and Statement II are false
  3. CStatement I is false but Statement II is true
  4. DBoth Statement I and Statement II are true

Correct answer

D. Both Statement I and Statement II are true

Step-by-step solution

Statement I: Total kinetic energy of a system equals _i 1 2 m_i v_i^2 . This is TRUE by definition. Statement II: Total KE can be decomposed as KE_ total = 1 2 M v_ cm ^2 + _i 1 2 m_i v_i'^2 , 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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