Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Solved Questions & Answers
Phase 1 – Page 3

This page focuses on multi-step IIT problems involving centre of mass velocity, acceleration, symmetry, and examiner traps.

Problem 9 (IIT–JEE Momentum + COM)

Question:
Two particles of masses m and 2m move along the same straight line with velocities u and 0 respectively. Find the velocity of the centre of mass of the system.

Solution:

Velocity of centre of mass is given by:

v_cm = (m×u + 2m×0) / (m + 2m)

v_cm = mu / 3m = u / 3

Answer: Velocity of centre of mass = u/3

IIT Tip: Always express answer in symbolic form when masses are variables.

Problem 10 (IIT–JEE Explosion with Motion)

Question:
A shell of mass M moving with velocity V explodes into two fragments of masses M/4 and 3M/4. If the smaller fragment comes to rest immediately after explosion, find the velocity of the larger fragment.

Solution:

Initial momentum of shell = M × V

Final momentum = (M/4 × 0) + (3M/4 × v)

By conservation of momentum:

M V = (3M/4) v

v = (4/3) V

Answer: Velocity of larger fragment = 4V/3

Examiner View: Students often forget initial momentum is not zero here.

Problem 11 (IIT–JEE COM Acceleration)

Question:
A system of particles is subjected to a net external force F. If the total mass of the system is M, find the acceleration of the centre of mass.

Solution:

According to Newton’s second law for a system:

F = M a_cm

a_cm = F / M

Answer: Acceleration of centre of mass = F / M

Problem 12 (IIT–JEE Boat–Man System)

Question:
A man walks from the rear to the front of a boat floating on still water. Describe the motion of the centre of mass of the system.

Solution:

There is no external horizontal force acting on the system.

Therefore, the horizontal position of the centre of mass remains unchanged.

While the man moves forward, the boat moves backward, keeping the centre of mass fixed.

Answer: Centre of mass remains at rest horizontally.

Problem 13 (IIT–JEE Symmetry Based)

Question:
Four equal masses are placed at the corners of a square. Find the position of the centre of mass.

Solution:

Due to symmetry, mass distribution is uniform.

Hence, the centre of mass lies at the point where the diagonals intersect.

Answer: Centre of mass is at the centre of the square.

IIT Examiner’s Golden Rules (Page 3)

✔ Always check if initial momentum is zero or not
✔ Explosion problems → momentum conservation first
✔ COM acceleration depends only on external force
✔ Symmetry can eliminate long calculations
✔ Symbolic answers preferred in IIT problems

📘 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