JEE Main 202622 JanuaryEvening Shift
- Exam
- JEE Main
- Year
- 2026
- Date
- 22 January
- Shift
- Evening Shift
- Subject
- Physics
- Chapter
- Center of Mass, Momentum and Collision
JEE Main 2026 · 22 January · Evening Shift · Physics · Center of Mass, Momentum and Collision
Given below are two statements : Statement I : For a mechanical...
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 :
Options
- AStatement I is true but Statement II is false
- BBoth Statement I and Statement II are false
- CStatement I is false but Statement II is true
- DBoth Statement I and Statement II are true
Correct answer
D. Both Statement I and Statement II are true
Step-by-step solution
Statement I: Total kinetic energy of a system equals . This is TRUE by definition.
Statement II: Total KE can be decomposed as , where the first term is kinetic energy of center of mass motion and the second is kinetic energy of particles relative to the center of mass. This is TRUE by the energy decomposition theorem (Koenig's theorem).
Both statements are true.
Statement II: Total KE can be decomposed as , where the first term is kinetic energy of center of mass motion and the second is kinetic energy of particles relative to the center of mass. This is TRUE by the energy decomposition theorem (Koenig's theorem).
Both statements are true.