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 :
Text Solution
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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.
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