Lesson 6 – Centre of Mass & System of Particles
IIT–JEE Tough Problems
Part 4 – Extreme Traps & Deep Reasoning
This part tests examiner psychology. Each problem looks simple but hides a dangerous conceptual trap.
Problem 16 (IIT–Advanced · Non-Inertial Frame)
A system of particles is observed from a frame accelerating horizontally with acceleration a. No real external force acts on the system. Describe the motion of the centre of mass in this frame.
Solution:
The frame is non-inertial.
A pseudo force of magnitude m a acts on each particle, opposite to the acceleration of the frame.
Net pseudo force on system = M a
Hence, centre of mass appears to accelerate opposite to the frame’s acceleration.
Answer:
COM accelerates with magnitude a
opposite to frame acceleration.
Trap: Zero real force ≠ zero acceleration in non-inertial frame.
Problem 17 (IIT–Advanced · Constraint + Rotation)
A rigid rod of mass M lies on a smooth horizontal surface. Equal and opposite forces are applied at its ends. Describe the motion of the centre of mass.
Solution:
Net external force = 0
Hence, acceleration of COM = 0
However, torque is non-zero.
Rod rotates about its centre of mass.
Answer:
Centre of mass remains at rest
while the rod rotates.
Problem 18 (IIT–Advanced · Moving Reference Trap)
A system moves with constant velocity relative to the ground. It is observed from another frame moving with constant velocity. Compare the centre of mass acceleration in both frames.
Solution:
Both frames are inertial.
Acceleration of COM depends only on net external force.
Since acceleration is zero in ground frame, it is also zero in the moving frame.
Answer:
COM acceleration is the same (zero) in both frames.
Problem 19 (IIT–Advanced · Variable Mass + COM)
A rocket moves in free space ejecting fuel symmetrically in opposite directions. Describe the motion of the centre of mass of the rocket–fuel system.
Solution:
Fuel ejection forces are internal to the system.
No external force acts on the rocket–fuel system.
Hence, centre of mass moves with constant velocity.
Answer:
COM moves uniformly in a straight line.
Problem 20 (IIT–Advanced · One-Line Killer)
State one condition under which the centre of mass of a system remains stationary.
Answer:
When the net external force on the system is zero and initial momentum is zero.
Exam Tip: IIT rewards short, law-based answers.
EXTREME-LEVEL THINKING RULES (Part–4)
✔ Identify inertial vs non-inertial frame first
✔ Pseudo force acts like external force in non-inertial frame
✔ Rotation ≠ translation of COM
✔ Equal & opposite forces may still rotate a body
✔ COM laws never fail — confusion comes from frame choice
📘 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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