Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Solved Questions & Answers
Phase 1 – Page 10 (Final Advanced Level)

This page contains final-level IIT–JEE problems that test deep understanding, option elimination, and examiner traps. These questions decide top ranks.

Problem 44 (IIT–Advanced – Multi Correct)

Question:
A system of particles is isolated in space. Which of the following statements are correct?

A) Total linear momentum remains constant
B) Centre of mass always remains at rest
C) Individual particles may accelerate
D) Centre of mass moves with uniform velocity

Solution:

A → True (no external force)
B → False (COM may move with constant velocity)
C → True (internal forces act)
D → True

Answer: A, C and D

Problem 45 (IIT–Advanced – Integer Type)

Question:
Two particles of masses 1 kg and 3 kg move along a straight line with velocities 8 m/s and −4 m/s respectively. Find the velocity of the centre of mass (in m/s).

Solution:

v_cm = (1×8 + 3×(−4)) / (1+3)

v_cm = (8 − 12) / 4 = −1

Answer: −1 m/s

Exam Tip: Sign of velocity matters — don’t ignore direction.

Problem 46 (IIT–Advanced – Explosion + Gravity)

Question:
A bomb explodes in mid-air into several fragments. Which statement correctly describes the motion of the centre of mass?

Solution:

Explosion produces only internal forces.

Gravity is the only external force.

Hence, centre of mass continues to move under gravity alone.

Answer: Centre of mass follows a parabolic trajectory.

Problem 47 (IIT–Advanced – Conceptual Depth)

Question:
Is it possible that the centre of mass of a system lies outside the system? Explain briefly.

Solution:

Centre of mass depends on mass distribution, not shape.

In hollow or ring-shaped bodies, mass surrounds empty space.

Answer: Yes, centre of mass may lie outside the body.

Problem 48 (IIT–Advanced – COM Acceleration Trap)

Question:
A system has zero net external force. Which of the following must be zero?

A) Velocity of centre of mass
B) Acceleration of centre of mass
C) Velocity of all particles
D) Momentum of individual particles

Solution:

Only acceleration of COM depends on net external force.

Answer: B

FINAL IIT SOLVER’S MENTAL FLOW (Page 10)

✔ Define the system clearly
✔ Identify only external forces
✔ Apply F = M a_cm immediately
✔ Use momentum conservation when F = 0
✔ Ignore internal force details completely
✔ Check symmetry before calculation
✔ Read options twice — traps are subtle

Lesson 6 – GRAND CONCLUSION

Centre of Mass is a logic chapter, not a formula chapter. Mastery comes from thinking at the system level. With Pages 1–10 completed, a student is now fully equipped for IIT-JEE Main & Advanced.