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Given below are two statements:
Statement I: For a mechanical system of many particles, the total kinetic energy is the sum of the kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of the kinetic energy of the centre of mass with respect to the origin and the kinetic energy of all the particles with respect to the centre of mass as the reference.
In the light of the above statements, choose the correct answer from the options given below:

Asked in JEE Main 22nd Jan 2nd Shift 2026 · Kinetic energy of a system of particles

• (1) Both Statement I and Statement II are false
• (2) Both Statement I and Statement II are true
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

Step-by-step solution

Why the other options are wrong

• (1) comes from doubting the plain additivity of kinetic energy, which needs no assumptions at all
• (3) comes from not recognising the second statement as König's theorem, which is a standard and exact result, not an approximation
• (4) comes from thinking kinetic energy is not simply additive because the particles interact. Interactions show up in the potential energy, never in the sum of 1/2 m v²

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