Lesson 6 – Centre of Mass & System of Particles
PHASE–2 : IIT–JEE Advanced Core Practice
Part 2 – Multi-Correct, Integer & Assertion Logic
Part–2 increases difficulty by introducing mixed constraints, symmetry traps, and option-wise elimination. These problems reflect IIT-Advanced marking logic.
Q1. (Multi-Correct | System Logic)
A system of particles is isolated. Which of the following statements are necessarily true?
A) Linear momentum of the system is conserved
B) Centre of mass has zero acceleration
C) Centre of mass must be at rest
D) Internal forces can change total momentum
Correct Options: A, B
Explanation:
• No external force ⇒ momentum conserved
• Zero net force ⇒ acm = 0
• COM may move with constant velocity (C false)
• Internal forces cannot change total momentum
Q2. (Integer Type | Sign Trap)
Three particles of masses 1 kg, 2 kg, and 3 kg move along x-axis with velocities 6 m/s, −3 m/s, and 0 m/s respectively. Find the velocity of centre of mass (m/s).
vcm = (1×6 + 2×(−3) + 3×0) / 6
vcm = (6 − 6) / 6 = 0
Answer: 0
Trap: Non-zero velocities ≠ moving COM
Q3. (Multi-Correct | Explosion + Gravity)
A projectile explodes into several fragments during flight. Which statements about the centre of mass are correct?
A) COM follows original projectile path
B) COM velocity changes suddenly at explosion
C) COM acceleration remains g downward
D) COM path depends on number of fragments
Correct Options: A, C
Explanation:
• Explosion = internal force only
• Gravity unchanged ⇒ same acceleration
• Number of fragments irrelevant
Q4. (Assertion–Reason | IIT Pattern)
Assertion (A): The centre of mass of a system may accelerate even when all particles have the same acceleration.
Reason (R): External force acting on the system determines acceleration of the centre of mass.
A) Both A and R are true and R is the correct explanation
B) Both A and R are true but R is not the explanation
C) A is true, R is false
D) A is false, R is true
Answer: A
Q5. (Multi-Correct | Force vs Torque Trap)
Two equal and opposite forces act on a rigid body at different points. Which of the following are correct?
A) Net external force is zero
B) Acceleration of COM is zero
C) The body may rotate
D) Linear momentum changes
Correct Options: A, B, C
Explanation:
• Translational effect cancels
• Torque may exist ⇒ rotation possible
• Momentum conserved
Q6. (Integer Type | COM Acceleration)
A system of total mass 10 kg is acted upon by a constant horizontal force of 20 N. Find the acceleration of the centre of mass (m/s²).
acm = F / M = 20 / 10 = 2
Answer: 2
PHASE–2 CORE STRATEGY (Part–2)
✔ Treat the entire system as a single particle
✔ Multi-correct ⇒ evaluate each option independently
✔ Integer type ⇒ direction & sign are critical
✔ Explosion never changes COM motion
✔ Rotation does not imply COM acceleration
Next in Phase–2
Part–3 will include:
• Very tough multi-correct sets
• Combined COM + Newton’s laws
• Advanced elimination techniques
📘 Centre of Mass & System of Particles – Complete Physics Library
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It includes theory, solved examples, objective questions, IIT-level problems, revision strategies, tricks, and exam-oriented guidance.
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