Lesson 6 – Centre of Mass & System of Particles
IIT–JEE Tough Problems
Part 9 – Ultimate PYQ-Style Mixed Set
This part simulates real IIT-Advanced thinking: mixed concepts, indirect COM usage, and tight option logic. Students must identify the governing principle before calculating.
Problem 41 (PYQ-Style · Hidden COM + Momentum)
A system consists of three particles of masses m, m, and 2m moving in a straight line with velocities u, −u, and 0 respectively. No external force acts on the system. Find the velocity of the system at any later time.
Solution:
Initial momentum: m·u + m·(−u) + 2m·0 = 0
Hence, velocity of centre of mass: vcm = 0
With no external force, COM velocity remains constant.
Answer:
Velocity of the system = 0
Problem 42 (PYQ-Style · Energy + COM Split)
Explain why in an isolated system, total kinetic energy can change even though the velocity of centre of mass remains constant.
Solution:
Total kinetic energy = KE of COM motion + KE of motion about COM.
In an isolated system, KE of COM motion remains constant.
Internal forces can change relative motion, hence KE about COM can change.
Answer:
KE can change due to internal energy redistribution
while COM motion remains unchanged.
Problem 43 (PYQ-Style · Frame Recognition)
A system is at rest in a train moving with constant velocity. Which statements are correct regarding the centre of mass?
A) COM is at rest in train frame
B) COM is moving in ground frame
C) COM acceleration is zero in both frames
D) COM momentum is zero in ground frame
Solution:
Train frame and ground frame are both inertial.
COM velocity differs between frames, but acceleration remains the same (zero).
Answer:
Correct options: A, B, C
Problem 44 (PYQ-Style · Explosion Trap)
A system initially at rest explodes into fragments. Immediately after explosion, which quantities are zero?
A) Total momentum
B) Velocity of centre of mass
C) Total kinetic energy
D) Acceleration of centre of mass
Solution:
No external force ⇒ momentum conserved.
Initial momentum = 0 ⇒ final momentum = 0.
Hence COM velocity remains zero.
Kinetic energy increases due to explosion.
Acceleration of COM is zero (no external force).
Answer:
Correct: A, B, D
Problem 45 (PYQ-Style · One-Line Law Application)
State the single condition under which the centre of mass of a system moves with constant velocity.
Answer:
When the net external force on the system is zero.
PYQ Insight: IIT often ends a section with a law-based one-liner.
PYQ DOMINATION STRATEGY (Part–9)
✔ Identify if the question is system-level
✔ If yes → immediately think COM
✔ Ask: external force present or not?
✔ Separate frame-dependent quantities from invariants
✔ Use energy split when momentum is conserved
✔ Finish with law-based clarity, not calculation
Why Part–9 Matters
This part mirrors how IIT-Advanced mixes simple laws with tricky wording. Students who master this rarely lose marks in COM-related questions.
📘 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
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Vision: Concept clarity • Logical thinking • Exam excellence
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