Lesson 6 – Centre of Mass & System of Particles

PHASE–2 : IIT–JEE Advanced Core Practice
Part 1 – Multi-Correct & Integer Type

Phase–2 problems are designed to test depth of understanding. Students must analyze system behaviour, not just apply formulas.

Q1. (Multi-Correct | IIT-Advanced)

A system of particles is isolated in space. Which of the following statements are correct?

A) Centre of mass moves with constant velocity
B) Total linear momentum remains constant
C) Individual particles cannot accelerate
D) Internal forces cannot change COM motion

Correct Options: A, B, D

Explanation:
• No external force ⇒ momentum conserved
• COM velocity remains constant
• Internal forces can accelerate particles, so C is false

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Q2. (Integer Type | IIT-Advanced)

Two particles of masses 3 kg and 1 kg move along x-axis with velocities 5 m/s and −3 m/s respectively. Find the velocity of the centre of mass (m/s).

v_cm = (3×5 + 1×(−3)) / 4

v_cm = (15 − 3) / 4 = 12 / 4 = 3

Answer: 3

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Q3. (Multi-Correct | Concept Trap)

A projectile explodes at the highest point of its path. Which statements about the centre of mass are correct?

A) COM follows the same parabolic path
B) COM comes to rest momentarily
C) COM acceleration is g downward
D) COM velocity becomes zero

Correct Options: A, C

Explanation:
• Explosion = internal force only
• Gravity remains the only external force
• COM never stops unless external force makes it stop

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Q4. (Integer Type | Direction Sensitive)

Two particles of masses 2 kg and 4 kg move along x-axis with velocities −6 m/s and +2 m/s. Find the velocity of centre of mass (m/s).

v_cm = (2×(−6) + 4×2) / 6

v_cm = (−12 + 8) / 6 = −4 / 6 = −2/3

Answer: −2/3

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Q5. (Multi-Correct | Force vs COM)

A system of particles is subjected to two equal and opposite external forces acting at different points. Which statements are correct?

A) Net external force is zero
B) COM acceleration is zero
C) System may rotate
D) Linear momentum changes

Correct Options: A, B, C

Explanation:
• Forces cancel translationally
• Torque may exist ⇒ rotation possible
• Momentum remains conserved

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PHASE–2 Thinking Strategy (Part 1)

✔ Always think at SYSTEM level first
✔ Check external force before calculations
✔ Multi-correct ⇒ check each option independently
✔ Integer type ⇒ sign and direction are crucial
✔ Explosion ≠ change in COM motion

Next in Phase–2

In Part 2, we will solve harder multi-correct questions, including mixed systems, symmetry traps, and Advanced-level eliminations.

📘 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

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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
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25. Part 25
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27. Part 27
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30. Part 30
31. Part 31
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33. Part 33
34. Part 34
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36. Part 36
37. Part 37
38. Part 38
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40. Part 40
41. Part 41
42. Part 42
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46. Part 46
47. Part 47
48. Part 48
49. Part 49
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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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