Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Solved Questions & Answers
Phase 1 – Page 2

This page contains higher-level IIT–JEE problems involving two-dimensional centre of mass, separation of particles, and momentum-based reasoning.

Problem 5 (IIT–JEE 2D Centre of Mass)

Question:
Three particles of masses m, 2m and 3m are placed at the points (0,0), (a,0) and (0,a) respectively. Find the coordinates of the centre of mass.

Solution:

x_cm = (m×0 + 2m×a + 3m×0) / (m + 2m + 3m)

x_cm = (2ma) / 6m = a/3

y_cm = (m×0 + 2m×0 + 3m×a) / 6m

y_cm = (3ma) / 6m = a/2

Answer: Centre of mass is at (a/3 , a/2)

IIT Tip: Always calculate x and y coordinates separately.

Problem 6 (IIT–JEE Explosion Concept)

Question:
A stationary shell explodes into two fragments of masses 1 kg and 3 kg. If the lighter fragment moves with a velocity of 12 m/s, find the velocity of the heavier fragment.

Solution:

Initial momentum of shell = 0

By conservation of momentum:

(1 × 12) + (3 × v) = 0

12 + 3v = 0

v = −4 m/s

Answer: Heavier fragment moves with velocity 4 m/s in opposite direction.

Examiner View: Always mention “initial momentum = 0”.

Problem 7 (IIT–JEE Motion of COM)

Question:
A man of mass m jumps vertically upward inside a freely falling lift. Describe the motion of the centre of mass of the man–lift system.

Solution:

The only external force acting on the system is gravity.

Internal forces between man and lift do not affect the motion of the centre of mass.

Hence, the centre of mass accelerates downward with acceleration g.

Answer: Centre of mass moves downward with acceleration g.

Problem 8 (IIT–JEE Velocity of COM)

Question:
Two particles of masses 4 kg and 2 kg move along a straight line with velocities 6 m/s and 0 m/s respectively. Find the velocity of centre of mass.

Solution:

v_cm = (4×6 + 2×0) / (4 + 2)

v_cm = 24 / 6 = 4 m/s

Answer: Velocity of centre of mass = 4 m/s

IIT Problem-Solving Rules (Page 2)

✔ Write momentum conservation clearly
✔ Identify external forces before solving
✔ Internal forces never affect COM motion
✔ Separate x and y directions in 2D problems
✔ Use symmetry whenever possible

📘 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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