Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Tough Problems
Part 8 – Hidden COM & Mixed-Concept Mastery

In real IIT-JEE questions, COM is rarely named directly. This part trains students to identify COM situations automatically inside momentum, energy, and motion problems.

Problem 36 (Hidden COM · Momentum)

Two blocks of masses m and 3m are moving on a smooth surface with velocities v and −v respectively. They collide elastically. Find the velocity of the system after collision.

Solution:

Total momentum before collision:

m·v + 3m·(−v) = −2mv

Velocity of centre of mass:

v_cm = (−2mv) / (4m) = −v/2

Since no external force acts, centre of mass velocity remains unchanged.

Answer:
Velocity of system (COM) after collision = −v/2

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Problem 37 (Hidden COM · Energy Trap)

A system of particles initially at rest explodes internally. Which quantities are conserved immediately after explosion?

A) Linear momentum
B) Kinetic energy
C) Centre of mass velocity
D) Mechanical energy

Solution:

Explosion produces only internal forces.

Linear momentum is conserved.

COM velocity remains zero.

Kinetic and mechanical energies change.

Answer:
Correct: A and C

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Problem 38 (COM + Energy View)

Explain why total kinetic energy of a system can be written as:

Total KE = KE of COM motion + KE about COM

Solution:

Any particle velocity can be written as: v = v_cm + v_relative

Squaring and summing over all particles splits total kinetic energy into two parts.

Answer:
KE naturally separates into COM motion and internal motion.

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Problem 39 (IIT–Advanced · Recognition Test)

A group of skaters push each other on frictionless ice. Which physical quantity governs the motion of the group as a whole?

Solution:

Forces between skaters are internal.

Motion of the group depends only on external forces.

Hence, centre of mass governs group motion.

Answer:
Motion is governed by the centre of mass.

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Problem 40 (COM Recognition · One-Line)

A system moves with constant velocity even though internal explosions keep occurring. Name the hidden principle.

Answer:

Conservation of centre of mass motion due to zero external force.

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HIDDEN COM RECOGNITION RULES (Part–8)

✔ If system motion is asked → think COM
✔ If internal forces dominate → COM law applies
✔ Explosions, collisions, pushes → COM hides inside
✔ Energy questions may still need COM separation
✔ Always ask: “Is this a system-level question?”

Why Part–8 is Crucial

Many students know COM formulas but fail to recognize COM situations. IIT rewards recognition more than calculation.

📘 Centre of Mass & System of Particles – Complete Physics Library

This library is a complete learning package for Intermediate + IIT JEE Physics covering Centre of Mass and System of Particles.

It includes theory, solved examples, objective questions, IIT-level problems, revision strategies, tricks, and exam-oriented guidance.

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📂 Stage 1: Intermediate Complete Notes (Concept Foundation)

1. Part 1
2. Part 2
3. Part 3
4. Part 4
5. Part 5
6. Part 6
7. Part 7
8. Part 8
9. Part 9
10. Part 10

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📂 Stage 2: Advanced Concepts & Applications

11. Part 11
12. Part 12
13. Part 13
14. Part 14
15. Part 15
16. Part 16
17. Part 17
18. Part 18
19. Part 19
20. Part 20

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📂 Stage 3: Objective Questions, Tough Problems & Revision

21. Part 21
22. Part 22
23. Part 23
24. Part 24
25. Part 25
26. Part 26
27. Part 27
28. Part 28
29. Part 29
30. Part 30
31. Part 31
32. Part 32
33. Part 33
34. Part 34
35. Part 35
36. Part 36
37. Part 37
38. Part 38
39. Part 39
40. Part 40
41. Part 41
42. Part 42
43. Part 43
44. Part 44
45. Part 45
46. Part 46
47. Part 47
48. Part 48
49. Part 49
50. Part 50
51. Part 51
52. Part 52
53. Part 53
54. Part 54
55. Part 55
56. Part 56
57. Part 57

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