Given below are two statements :
Statement I : For a mechanical system of many particles total kine

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 :

Professor PC Thomas Classes · Answer

Statement I is true as the total kinetic energy of a system is fundamentally the scalar sum of the kinetic energies of its constituent particles. Statement II is also true; this is known as Koenig's Theorem, which mathematically separates the total kinetic energy into the translational kinetic energy of the center of mass and the internal kinetic energy of the particles relative to the center of mass ($K_{total} = K_{cm} + K_{internal}$).