Lesson 6 – Centre of Mass & System of Particles
IIT–JEE Tough Problems
Part 6 – Final Boss (Rank <100 Level)
This part contains conceptual paradoxes and examiner-designed illusion questions. If a student understands these, Centre of Mass is permanently mastered.
Problem 26 (IIT–Advanced · Conceptual Paradox)
A system of particles has zero net external force at all times. Is it possible that the centre of mass has a non-zero velocity and changing direction? Explain.
Solution:
Zero net external force implies:
acm = 0
Hence, velocity of centre of mass must be constant in both magnitude and direction.
Change in direction implies acceleration, which contradicts zero external force.
Answer:
No. Direction of COM velocity cannot change.
Why this is deadly: Many students confuse particle motion with COM motion.
Problem 27 (IIT–Advanced · Frame Illusion)
A system is at rest relative to an accelerating frame. Describe the motion of its centre of mass as seen from an inertial frame.
Solution:
If the system is at rest in an accelerating frame, it must have the same acceleration as that frame.
Ground frame is inertial.
Hence, centre of mass accelerates with the acceleration of the frame.
Answer:
COM accelerates with the same acceleration as the frame.
Problem 28 (IIT–Advanced · No-Calculation Killer)
Two identical particles move in opposite directions with equal speeds. Can the centre of mass be accelerating? Justify without calculation.
Solution:
Acceleration of centre of mass depends only on net external force.
Motion of particles does not matter.
Without external force, COM cannot accelerate.
Answer:
No, centre of mass cannot accelerate.
Problem 29 (IIT–Advanced · Time Logic Trap)
A system initially has zero momentum. A constant external force acts for a short time. At a later instant, momentum again becomes zero. Is the acceleration of centre of mass zero at that later instant?
Solution:
Acceleration depends on force, not on instantaneous momentum.
If external force still acts, acceleration is non-zero even if momentum is zero.
Answer:
No. Acceleration may be non-zero.
Rank-100 Insight: Momentum value ≠ force acting at that instant.
Problem 30 (IIT–Advanced · Ultimate Law Test)
Write the most general statement governing the motion of centre of mass that applies in all frames.
Answer:
In an inertial frame:
Fexternal = M acm
In a non-inertial frame:
Pseudo forces must be included
as external forces.
Master Statement: Laws do not fail — frames change interpretation.
FINAL RANK <100 MINDSET (Lesson 6)
✔ Never ask “what are particles doing?” first
✔ Always ask “what are external forces?” first
✔ Acceleration depends on force, not velocity or momentum
✔ Frame confusion causes most errors
✔ If stuck, write F = M acm calmly
✔ Confidence + clarity beats speed
🏁 FINAL CLOSURE – LESSON 6
With Tough Parts 1–6 completed, Lesson 6 is now covered at a level that matches or exceeds India’s top coaching institutes.
This content does not just prepare students for IIT-JEE — it trains them to think like physicists.
📘 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.
📂 Stage 1: Intermediate Complete Notes (Concept Foundation)
📂 Stage 2: Advanced Concepts & Applications
📂 Stage 3: Objective Questions, Tough Problems & Revision
🔗 Learning Hub & Community
Prepared by: Shaktimatha Learning 🌱
Vision: Concept clarity • Logical thinking • Exam excellence
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