Lesson 6 – Centre of Mass & System of Particles
IIT–JEE Tough Problems
Part 5 – Final Killer Set (Rank <200 h3="" level="">
This is the final and hardest set for Centre of Mass. These problems test whether a student can see through traps and apply laws calmly under pressure.
Problem 21 (IIT–Advanced · Hidden Constraint)
Two identical blocks are connected by a light spring and placed on a smooth horizontal surface. The spring is compressed and the system is released. At some instant, both blocks have equal speeds. Find the velocity of the centre of mass at that instant.
Solution:
Spring force is internal.
No external horizontal force acts on the system.
Hence, velocity of centre of mass remains constant throughout the motion.
If system was initially at rest, COM velocity remains zero at all times.
Answer:
Velocity of centre of mass = 0
Trap: “Equal speeds” tempts calculation — but COM law kills it instantly.
Problem 22 (IIT–Advanced · Pseudo Force Paradox)
A system of particles is at rest in a lift accelerating upward with acceleration a. Find the acceleration of the centre of mass as observed from the ground frame.
Solution:
Ground frame is inertial.
Lift applies an upward external force on the system.
Hence, centre of mass accelerates upward with acceleration a.
Answer:
Acceleration of COM = a upward
Insight: “Rest in lift” does NOT mean rest in inertial frame.
Problem 23 (IIT–Advanced · COM Path Trap)
A projectile explodes at the highest point of its trajectory into many fragments which scatter in all directions. Describe the path of the centre of mass.
Solution:
Explosion involves only internal forces.
Gravity remains the only external force.
Therefore, centre of mass continues the same parabolic motion as before explosion.
Answer:
COM follows the same parabola.
Problem 24 (IIT–Advanced · Absolute Killer)
Can the centre of mass of a system accelerate while the total momentum of the system is zero? Justify clearly.
Solution:
Yes, it is possible.
Zero momentum does NOT imply zero external force.
Example: a system initially at rest (zero momentum) subjected to a non-zero external force.
Momentum changes with time, hence centre of mass accelerates.
Answer:
Yes, COM can accelerate even if momentum is initially zero.
Topper Insight: Always distinguish between “value now” and “rate of change”.
Problem 25 (IIT–Advanced · One-Line Law Test)
Write the most fundamental equation governing the motion of centre of mass of a system.
Answer:
Fexternal = M acm
Exam Tip: This one line can solve 70% of COM questions.
FINAL TOPPER RULES (Lesson 6)
✔ First write F = M acm
✔ Ask: external force present or not?
✔ Explosion, springs, tension → internal only
✔ Frame confusion creates 90% mistakes
✔ Never calculate before applying COM law
✔ Calm thinking beats speed in IIT-Advanced
Lesson 6 – COMPLETE CLOSURE
With Tough Parts 1–5 completed, Lesson 6 (Centre of Mass & System of Particles) is now covered at a level stronger than most coaching institutes.
📘 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
No comments:
Post a Comment