JEE Main 2026 — Jan 22, Shift 2 — Physics solution

JEE Main2026Jan 22, Shift 2Physics

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. 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
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

Solution

Statement I — trivially correct from the definition: $K E = i \sum \frac{1}{2} m_{i} v_{i}^{2}$ .

Statement II — for a two-particle system this is the well-known König decomposition:

$K E = \frac{1}{2} (m_{1} + m_{2}) v_{c m}^{2} + \frac{1}{2} \frac{m _{1} m _{2}}{m _{1} + m _{2}} ∣ v_{1} - v_{2} ∣^{2}$ .

The second term is the kinetic energy of the particles in the COM frame. The result generalises to any number of particles, so Statement II is correct.

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