Lesson 6 – Centre of Mass & System of Particles

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

This section contains IIT–JEE level solved problems on Centre of Mass. Each problem is solved using standard IIT methods, focusing on concept, reasoning, and correctness.

Problem 1 (IIT–JEE Type)

Question:
Two particles of masses 2 kg and 3 kg are moving along a straight line with velocities 4 m/s and −2 m/s respectively. Find the velocity of the centre of mass of the system.

Solution:

Velocity of centre of mass is given by:

v_cm = (m₁v₁ + m₂v₂) / (m₁ + m₂)

v_cm = (2×4 + 3×(−2)) / (2+3)

v_cm = (8 − 6) / 5 = 2 / 5 = 0.4 m/s

Answer: Velocity of centre of mass = 0.4 m/s

IIT Tip: For COM velocity questions, directly use momentum conservation.

Problem 2 (IIT–JEE Conceptual)

Question:
A shell explodes into two fragments in mid-air. Neglecting air resistance, describe the motion of the centre of mass after explosion.

Solution:

Explosion is caused by internal forces only. Internal forces cannot change the motion of the centre of mass.

The only external force acting on the system is gravity. Hence, the centre of mass continues to move under gravity alone.

Therefore, the centre of mass follows the same parabolic path as it would have followed without explosion.

Answer: The centre of mass continues in a parabolic path.

Examiner View: Words like internal force and external force must appear for full marks.

Problem 3 (IIT–JEE Numerical)

Question:
Three particles of equal mass are placed at the vertices of an equilateral triangle of side a. Find the position of the centre of mass.

Solution:

Due to symmetry, the centre of mass lies at the centroid of the triangle.

The centroid is the point where the medians intersect.

Answer: Centre of mass is at the centroid of the triangle.

IIT Shortcut: For symmetric systems, always look for symmetry before calculations.

Problem 4 (IIT–JEE Motion of COM)

Question:
A man jumps horizontally from a stationary boat in still water. Describe the motion of the centre of mass of the man–boat system.

Solution:

There is no external horizontal force acting on the system. Hence, the horizontal velocity of centre of mass remains zero.

As a result, while the man and boat move in opposite directions, the centre of mass remains at the same position relative to water.

Answer: Centre of mass remains stationary.

Key IIT Solving Rules (Must Remember)

✔ Motion of COM depends only on external forces
✔ Internal forces never affect COM motion
✔ Use momentum conservation for COM velocity
✔ Symmetry simplifies most IIT problems