Lesson 6 – Centre of Mass & System of Particles
IIT–JEE Tough Problems
Part 3 – Ultra-Hard Mixed Constraints
This part contains concept-dominated, time-evolution problems. These are not formula questions — they test thinking, patience, and system-level clarity.
Problem 11 (IIT–Advanced · Constraint + COM)
Two blocks of masses m and 2m are connected by a light string and placed on a smooth horizontal surface. A constant horizontal force F is applied on the block of mass m. Find the acceleration of the centre of mass of the system.
Solution:
Total mass of system = m + 2m = 3m
External force on system = F
Using Newton’s law for the system:
acm = F / (3m)
Answer:
Acceleration of centre of mass = F / (3m)
Key Trap: String tension is internal — never include it in COM equation.
Problem 12 (IIT–Advanced · Symmetry Killer)
Four identical particles are placed at the four corners of a square. They are projected simultaneously with equal speeds, each towards the centre of the square. Describe the motion of the centre of mass.
Solution:
By symmetry, all momenta cancel pairwise.
Net external force = 0
Initial momentum of system = 0
Hence, centre of mass remains at rest at the centre.
Answer:
Centre of mass remains stationary at the centre.
Problem 13 (IIT–Advanced · Variable Mass Logic)
A cart of mass M moves on a frictionless surface with velocity v. Sand is dropped vertically into the cart at a constant rate. Find the horizontal velocity of the centre of mass of the system.
Solution:
Sand enters with zero horizontal velocity.
No external horizontal force acts on the system.
Hence, horizontal momentum of the system is conserved.
Therefore, velocity of centre of mass remains constant.
Answer:
Horizontal velocity of COM = v
Problem 14 (IIT–Advanced · Time Evolution)
A system of particles initially at rest experiences a constant external force F for time t and then the force is removed. Describe the motion of the centre of mass after force removal.
Solution:
During force application: acm = F / M
Velocity gained: v = (F / M) t
After force removal: Net external force = 0
Hence COM moves with constant velocity v.
Answer:
COM moves uniformly with velocity (F t / M).
Problem 15 (IIT–Advanced · Conceptual Depth)
Can the centre of mass of a system follow a straight line while individual particles follow curved paths? Justify your answer.
Solution:
Motion of centre of mass depends only on external forces.
Individual particles may experience internal forces causing curved motion.
Hence, COM may follow a straight line while particles move along curved paths.
Answer:
Yes, such motion is possible.
ULTRA-HARD SOLVER RULES (Part–3)
✔ Always define system boundary first
✔ Separate external and internal forces strictly
✔ Use symmetry wherever possible
✔ Variable mass does not break COM laws
✔ Think in time-segments (before / during / after)
📘 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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