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:
- (A)Both Statement I and Statement II are true✓ Correct
- (B)Statement I is true but Statement II is false
- (C)Statement I is false but Statement II is true
- (D)Both Statement I and Statement II are false
Answer: (A)
Solution
The total kinetic energy of a system of particles is the arithmetic sum of the individual kinetic energies, , so Statement I is correct. By Koenig's theorem the same total separates into the kinetic energy of the whole mass moving with the centre of mass and the kinetic energy of the particles measured relative to the centre of mass, so Statement II is correct as well. Both statements are true.
JEE Main · 2026 · 22 Jan 2026 · Shift 2 · Single correct option