Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Solved Questions & Answers
Phase 1 – Page 9 (PYQ-Level Practice)

This page is designed to simulate actual IIT-JEE PYQs. Students must apply system-level Newton’s laws, vector reasoning, and elimination of traps.

Problem 39 (PYQ-Type – Integer Answer)

Question:
Two particles of masses 2 kg and 4 kg are moving along x-axis with velocities 6 m/s and −2 m/s respectively. Find the velocity of the centre of mass (in m/s).

Solution:

v_cm = (2×6 + 4×(−2)) / (2+4)

v_cm = (12 − 8) / 6 = 4 / 6 = 2 / 3

Answer: 2/3 m/s

PYQ Tip: Integer-type answers may be fractional.

Problem 40 (PYQ-Type – Multi Correct)

Question:
A system of particles is isolated. Which of the following statements are correct?

A) Centre of mass moves with constant velocity
B) Individual particles cannot accelerate
C) Internal forces do not affect COM motion
D) Momentum of the system is conserved

Solution:

A → True (no external force)
B → False (internal forces can accelerate particles)
C → True
D → True

Answer: A, C and D

Problem 41 (PYQ-Type – Explosion in Motion)

Question:
A projectile moving with velocity u explodes into two fragments. One fragment comes to rest immediately. Find the velocity of the other fragment if masses are equal.

Solution:

Initial momentum = m u

Final momentum = m × 0 + m × v

By conservation of momentum:

m u = m v ⇒ v = u

Answer: Velocity of moving fragment = u

Examiner Trap: COM velocity remains unchanged even though fragments behave differently.

Problem 42 (PYQ-Type – COM Acceleration)

Question:
A system of total mass M is subjected to a constant force F. Find the acceleration of the centre of mass.

Solution:

a_cm = F / M

Answer: F / M

Problem 43 (PYQ-Type – Conceptual)

Question:
A system has zero external force acting on it. Can the centre of mass be at rest while all particles are moving?

Solution:

Yes. Motion of COM depends on net external force, not individual particle velocities.

For example, two equal masses moving with equal speed in opposite directions.

Answer: Yes, COM can be at rest while particles move.

Final PYQ Strategy (Page 9)

✔ Treat the entire system as one particle of mass M
✔ Apply momentum conservation wherever possible
✔ Separate internal vs external forces clearly
✔ Don’t assume COM motion from particle motion
✔ Read PYQ options very carefully

End of Phase 1 – IIT Mastery

With this page, students complete a full IIT-level mastery cycle for Centre of Mass — from basics to PYQ dominance.

📘 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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1. Part 1
2. Part 2
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📂 Stage 3: Objective Questions, Tough Problems & Revision

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