Lesson 6 – Centre of Mass & System of Particles

IIT–JEE Solved Questions & Answers
Phase 1 – Page 4

This page includes high-difficulty IIT problems where centre of mass, momentum, symmetry, and external forces are tested together. Students must focus on logic, not memorization.

Problem 14 (IIT–JEE Mixed Concept)

Question:
Two particles of masses m and 3m are connected by a light string and placed on a smooth horizontal surface. A horizontal force F is applied on the particle of mass m. Find the acceleration of the centre of mass of the system.

Solution:

Total mass of the system = m + 3m = 4m

Net external force acting on the system = F

Acceleration of centre of mass:

a_cm = F / (4m)

Answer: Acceleration of centre of mass = F / 4m

IIT Insight: Distribution of force inside system does not matter.

Problem 15 (IIT–JEE Rocket-Type Thinking)

Question:
A system consists of a block and sand falling vertically under gravity. Sand leaks out uniformly from the block. Describe the motion of the centre of mass of the system.

Solution:

The only external force acting on the system is gravity.

Loss of sand is an internal process for the system.

Hence, the centre of mass accelerates downward with acceleration g.

Answer: Centre of mass moves downward with acceleration g.

Examiner Warning: Variable mass does NOT automatically change COM acceleration.

Problem 16 (IIT–JEE Relative Motion Trap)

Question:
Two identical particles move towards each other with equal speeds. What is the velocity of the centre of mass?

Solution:

Let velocities be +v and −v.

v_cm = (m×v + m×(−v)) / (2m) = 0

Answer: Centre of mass remains at rest.

Problem 17 (IIT–JEE Geometry + COM)

Question:
Four equal masses are placed at three vertices of an equilateral triangle and one mass at its centre. Find the position of the centre of mass.

Solution:

Due to symmetry, the masses at vertices balance each other.

The mass at the centre dominates symmetry.

Answer: Centre of mass lies at the centre of the triangle.

Problem 18 (IIT–JEE Force Direction Trap)

Question:
A system of particles is subjected to two equal and opposite forces acting at different points. What is the acceleration of the centre of mass?

Solution:

Net external force on system = 0

Hence, acceleration of centre of mass = 0

Answer: Centre of mass moves with constant velocity.

IIT Trap: Forces acting at different points still cancel vectorially.

IIT Examiner’s Master Rules (Page 4)

✔ Acceleration of COM = (Net external force) / (Total mass)
✔ Internal distribution of forces does not matter
✔ Variable mass ≠ variable COM acceleration automatically
✔ Symmetry can beat long calculations
✔ Always separate internal vs external forces