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Physics · System Of Particles

JEE Main 2026 — 22 January, Evening Shift — Question 41

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II :

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 canter of mass w.r.t. to the origin and the kinetic energy of all the particles w.r.t. the canter of mass as the reference.

In the light of the above statements, choose the correct answer from the options given below :

  1. Option A:

    Both Statement I and Statement II are true

    Correct
  2. Option B:

    Statement I is true but Statement II is false

  3. Option C:

    Statement I is false but Statement II is true

  4. Option D:

    Both Statement I and Statement II are false

Answer: A

Step-by-step solution

KE=12m1v12+12m2v22K E=\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2} KE=12( m1+m2)vcm2+12 m1 m2 m1+m2∣v→1−v→2∣2\mathrm{KE}=\frac{1}{2}\left(\mathrm{~m}_{1}+\mathrm{m}_{2}\right) \mathrm{v}_{\mathrm{cm}}^{2}+\frac{1}{2} \frac{\mathrm{~m}_{1} \mathrm{~m}_{2}}{\mathrm{~m}_{1}+\mathrm{m}_{2}}\left|\overrightarrow{\mathrm{v}}_{1}-\overrightarrow{\mathrm{v}}_{2}\right|^{2}

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
22 January, Evening Shift
Subject
Physics
Chapter
System Of Particles
Topic
Motion of Center of Mass & Frame of CM

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