Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Tough Problems
Part 2 – Rank-Maker Multi-Step Numericals

These problems require clean system definition, vector momentum conservation, and calm step-by-step execution.

Problem 6 (IIT–Advanced · Explosion + Geometry)

A particle of mass 3m moving with velocity u along x-axis explodes into three equal fragments at the origin. Two fragments move along +y and −y directions with speed u. Find the velocity of the third fragment.

Solution:

Initial momentum = 3m·u î

Momentum after explosion (y-direction): m·u − m·u = 0 (balanced)

Let velocity of third fragment = v î

Momentum conservation (x-direction): m·v = 3m·u

v = 3u

Answer: Velocity of third fragment = 3u î

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Problem 7 (IIT–Advanced · Boat + Man + Return)

A man of mass m walks from one end of a boat (mass 2m, length L) to the other end and then returns back to the starting point. Find the net displacement of the boat.

Solution:

No external horizontal force → COM fixed.

Forward journey: Boat shifts by L/3 backward.

Return journey: Boat shifts by L/3 forward.

Net displacement of boat = 0

Answer: 0

Insight: COM logic applies to the entire process, not just one motion.

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Problem 8 (IIT–Advanced · Variable Force)

A system of total mass M is acted upon by a time-varying external force F(t). Find the acceleration of the centre of mass.

Solution:

Newton’s law for system: F(t) = M a_cm(t)

a_cm(t) = F(t) / M

Answer: a_cm(t) = F(t)/M

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Problem 9 (IIT–Advanced · Rotating System Trap)

A rigid body rotates freely about its centre of mass. Which of the following quantities remain zero?

A) Net external force
B) Linear momentum of the system
C) Acceleration of centre of mass

Solution:

Rotation does not imply translation.

Net external force = 0 ⇒ Linear momentum constant (zero if initially zero) ⇒ COM acceleration = 0

Answer: All three remain zero.

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Problem 10 (IIT–Advanced · Gravity + Explosion)

A projectile explodes into two fragments in mid-air. One fragment falls vertically downward. Describe the motion of the centre of mass.

Solution:

Explosion = internal force only.

Only external force is gravity.

Hence COM continues to follow the same parabolic path as the original projectile.

Answer: Centre of mass follows original parabolic trajectory.

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TOUGH PROBLEM MASTER STRATEGY (Part–2)

✔ Always resolve momentum into components
✔ Treat explosion problems vector-wise
✔ COM logic applies to entire motion history
✔ Rotation does NOT imply COM motion
✔ Time-varying forces still obey F = Ma for COM

📘 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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Prepared by: Shaktimatha Learning 🌱
Vision: Concept clarity • Logical thinking • Exam excellence