Lesson 6 – Centre of Mass & System of Particles
IIT–JEE Solved Questions & Answers
Phase 1 – Page 5
This page represents high-end IIT–JEE Advanced problems where students must combine centre of mass, momentum, force analysis, symmetry, and examiner traps.
Problem 19 (IIT–JEE Advanced – Force Redistribution)
Question:
Three blocks of masses m, m, and 2m are placed in contact on a smooth
horizontal surface.
A horizontal force F is applied on the block of mass 2m.
Find the acceleration of the centre of mass of the system.
Solution:
Total mass of the system = m + m + 2m = 4m
Net external force acting on the system = F
Acceleration of centre of mass:
acm = F / (4m)
Answer: Acceleration of centre of mass = F / 4m
IIT Insight: Which block receives the force does not matter for COM acceleration.
Problem 20 (IIT–JEE Advanced – Zero Net Force)
Question:
A system of particles is subjected to two unequal forces acting
in opposite directions.
Under what condition will the centre of mass have zero acceleration?
Solution:
Acceleration of centre of mass depends on net external force.
If the vector sum of external forces is zero, acceleration of centre of mass is zero.
Answer: Centre of mass has zero acceleration when net external force is zero.
Problem 21 (IIT–JEE Advanced – Lift & Jump)
Question:
A person jumps upward inside a lift accelerating upward with acceleration a.
Find the acceleration of the centre of mass of the person–lift system.
Solution:
The only external forces acting on the system are gravitational force and the normal reaction from the supporting cable.
Internal forces between person and lift do not affect COM motion.
Therefore, acceleration of centre of mass equals acceleration of the lift system, which is a.
Answer: Acceleration of centre of mass = a
Problem 22 (IIT–JEE Advanced – Geometry + COM)
Question:
Four equal masses are placed at the midpoints of the sides of a square.
Find the position of the centre of mass.
Solution:
The mass distribution is symmetric about both diagonals.
Hence, the centre of mass lies at the centre of the square.
Answer: Centre of mass is at the geometric centre of the square.
Problem 23 (IIT–JEE Advanced – Conceptual Trap)
Question:
Can the centre of mass of a system be outside the material
points of the system? Explain with reasoning.
Solution:
Centre of mass is a mathematical point determined by mass distribution.
In hollow bodies like rings or shells, mass surrounds empty space.
Hence, the centre of mass lies in empty space.
Answer: Yes, centre of mass can lie outside the body.
IIT Examiner’s Final Checklist (Page 5)
✔ Acceleration of COM = Net external force / Total mass
✔ Internal force location never matters
✔ Variable mass ≠ variable COM motion automatically
✔ Symmetry saves time in Advanced problems
✔ Explain reasoning clearly – marks depend on logic
📘 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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