Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Solved Questions & Answers
Phase 1 – Page 6 (Final Capstone)

This page completes the IIT/JEE solved section with extreme reasoning problems, hidden traps, and a final solver’s framework used by toppers.

                                         

Problem 24 (IIT–Advanced – Multi-Force System)

Question:
A system of particles is acted upon by gravity and an external horizontal force F. If total mass of the system is M, find the acceleration of the centre of mass.

Solution:

External forces acting on the system are:
• Horizontal force F
• Vertical force Mg (gravity)

Hence, acceleration of centre of mass has two components:

a_x = F / M
a_y = g

Answer:
Centre of mass accelerates with components (F/M , g).

IIT Insight: Always resolve COM acceleration into components.

Problem 25 (IIT–Advanced – Sudden Separation)

Question:
Two blocks connected by a light spring are moving with velocity V. The spring suddenly breaks. Describe the motion of the centre of mass.

Solution:

Spring force is internal to the system.

No external force acts during the breaking process.

Therefore, velocity of centre of mass remains unchanged.

Answer:
Centre of mass continues to move with constant velocity V.

Problem 26 (IIT–Advanced – COM Outside Body)

Question:
A semicircular wire of uniform mass distribution is placed on a table. Where does its centre of mass lie?

Solution:

Due to symmetry, centre of mass lies along the axis of symmetry.

For a semicircular wire, centre of mass lies inside the empty region, not on the wire itself.

Answer:
Centre of mass lies on the axis of symmetry, inside the semicircle.

Problem 27 (IIT–Advanced – Zero External Force)

Question:
A system of particles is isolated. Can individual particles accelerate while the centre of mass moves with constant velocity? Explain.

Solution:

In an isolated system, net external force is zero.

Hence, centre of mass moves with constant velocity.

However, internal forces can accelerate individual particles.

Answer:
Yes, particles can accelerate while COM moves uniformly.

Problem 28 (IIT–Advanced – Examiner Trap)

Question:
A system experiences zero acceleration of centre of mass. Does it imply zero external force? Justify.

Solution:

From Newton’s law:
F_ext = M a_cm

If a_cm = 0, then F_ext = 0.

Answer:
Yes, zero acceleration of COM implies zero net external force.

Final IIT Solver’s Framework (Lesson 6)

✔ Step 1: Identify system boundaries clearly
✔ Step 2: List all external forces only
✔ Step 3: Use F = M a_cm without hesitation
✔ Step 4: Ignore all internal forces instantly
✔ Step 5: Apply symmetry wherever possible
✔ Step 6: Separate x & y directions in 2D problems

Lesson 6 – Final Takeaway

Centre of Mass is not a formula chapter. It is a thinking chapter. IIT examiners test how quickly you can separate internal and external forces and apply Newton’s laws at the system level.