Lesson 6 – Centre of Mass & System of Particles

Objective Type Questions & Answers – Set 5 (IIT-JEE Advanced – Final Level)

This set represents final-stage objective practice. Each question tests deep understanding of external forces, momentum conservation, and COM motion.

Advanced Conceptual MCQs

1. A system of particles is moving under no external force. Which of the following quantities must remain constant?

A) Velocity of each particle
B) Momentum of each particle
C) Velocity of centre of mass
D) Kinetic energy of the system

Answer: C

Explanation: With zero external force, COM velocity remains constant.

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2. A body explodes at the highest point of its projectile motion. Immediately after explosion, the centre of mass:

A) Moves vertically downward
B) Comes to rest momentarily
C) Continues along the original parabolic path
D) Moves horizontally

Answer: C

Explanation: Explosion is internal; gravity is the only external force.

Numerical Objective Questions (Momentum Based)

3. Two particles of masses 3 kg and 1 kg move along x-axis with velocities 2 m/s and 6 m/s respectively. The velocity of centre of mass is:

A) 2 m/s
B) 3 m/s
C) 4 m/s
D) 5 m/s

Answer: C

Explanation:
v_cm = (3×2 + 1×6) / (3+1) = (6 + 6) / 4 = 3 m/s ❌
Careful! Re-check: correct arithmetic gives 3 m/s.
Correct option → B

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4. Three particles of equal mass are placed at (−a,0), (a,0) and (0,a). The coordinates of centre of mass are:

A) (0, a/3)
B) (a/3, a/3)
C) (0, 0)
D) (a/2, a/2)

Answer: A

Explanation:
x_cm = (−a + a + 0)/3 = 0
y_cm = (0 + 0 + a)/3 = a/3

Assertion – Reason (IIT Advanced)

5. Assertion (A): The centre of mass of a system may accelerate even if no particle accelerates relative to another.
Reason (R): External force can accelerate all particles equally.

A) Both A and R are true and R is correct explanation
B) Both A and R are true but R is not explanation
C) A is true, R is false
D) A is false, R is true

Answer: A

IIT Trap / Thinking Questions

6. A man jumps vertically upward inside a freely falling lift. The centre of mass of man–lift system:

A) Moves upward
B) Moves downward with acceleration g
C) Remains at rest
D) Moves upward with acceleration g

Answer: B

Explanation: Only external force is gravity acting on total mass.

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7. A rocket ejects fuel in deep space (no gravity). The centre of mass of rocket–fuel system:

A) Accelerates forward
B) Accelerates backward
C) Remains at rest or moves uniformly
D) Oscillates

Answer: C

One-Line Kill Points (IIT Memory)

• External force = M × a_cm
• Explosion does NOT change COM motion
• COM motion ignores internal forces
• Projectile COM follows same trajectory always

Final IIT Solver’s Checklist

✔ Ask: external force present or not?
✔ If no → COM velocity constant
✔ Use momentum conservation directly
✔ Separate x and y in 2D instantly
✔ Explosion ≠ acceleration of 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