Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Tough Problems
Part 7 – Advanced Extensions & Conceptual Maturity

This part sharpens the student’s ability to reason without heavy calculation. IIT-Advanced often rewards this kind of thinking.

Problem 31 (Impulse + COM)

A system of particles initially has zero momentum. A very large force acts for a very small time on one particle. Describe the effect on the centre of mass.

Solution:

Large force acting for small time produces finite impulse.

Impulse equals change in momentum of the system.

Hence, centre of mass velocity changes instantaneously.

Answer:
COM velocity changes suddenly due to impulse.

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Problem 32 (Limit Argument)

Consider a system of N identical particles arranged symmetrically. As N → ∞, describe the behaviour of the centre of mass.

Solution:

By symmetry, all contributions cancel pairwise.

Net external force remains zero.

Hence, centre of mass remains fixed.

Answer:
COM stays stationary due to perfect symmetry.

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Problem 33 (COM vs Geometrical Centre)

A body has uniform shape but non-uniform mass density. Where is its centre of mass located?

Solution:

COM depends on mass distribution, not geometry alone.

Hence, it need not coincide with geometrical centre.

Answer:
COM shifts toward regions of higher mass density.

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Problem 34 (Zero Momentum ≠ Rest)

A system has zero total momentum at an instant. Can its centre of mass be moving at that instant?

Solution:

Momentum of system = M v_cm.

If momentum is zero, v_cm must be zero.

Hence, COM cannot be moving at that instant.

Answer:
No. Zero momentum implies zero COM velocity.

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Problem 35 (Qualitative Master Question)

Why is centre of mass analysis preferred over individual particle analysis in multi-body systems?

Solution:

Individual particle motion is complicated by internal forces.

COM motion depends only on external forces.

Hence, COM simplifies analysis drastically.

Answer:
COM reduces a many-body problem to a single-body problem.

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ADVANCED THINKING RULES (Part–7)

✔ Use impulse when force acts briefly
✔ Symmetry can replace calculation
✔ Geometry alone never decides COM
✔ Zero momentum has immediate meaning
✔ COM thinking simplifies complex systems

Why This Part Exists

Part–7 trains students to think like physicists, not just exam-solvers. This is the hidden layer of IIT preparation.

📘 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
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7. Part 7
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📂 Stage 3: Objective Questions, Tough Problems & Revision

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