Physics · System Of Particles And Rotational Motion · NEET
The centre of mass (COM) moves as if all the mass of the system were placed at that one point and every external force acted there. Its velocity is V = (m1v1 + m2v2 + ...)/M, and only a net EXTERNAL force can change this velocity (M A = F_external). Memory hook: "Inside pushes never move the COM; only an outside push does." So if two particles pull each other but no outside force acts, the COM keeps its original velocity, even zero.
Internal attraction gives A (3m) speed v and B (m) speed 3v, so their momenta cancel (3m·v = m·3v). Total momentum is zero, so the centre of mass stays fixed at V = 0.
Your doubts, answered
Can an internal force move the centre of mass?
No. Internal forces (like two particles pulling each other, or the push during an explosion) always come in equal and opposite pairs, so they cancel in the sum. Only the net EXTERNAL force can accelerate the COM: M A = F_external. This is why the COM path never bends because of internal forces.
Why is the velocity of the centre of mass zero when two particles attract each other from rest?
They start at rest, so total momentum P = 0. The attraction between them is an internal force, so no external force acts on the system. Since P = M V stays constant and started at 0, V of the COM stays zero the whole time, no matter how fast each particle moves.
What is the exact formula for the velocity of the centre of mass?
V = (m1 v1 + m2 v2 + ... + mn vn) / M, where M = m1 + m2 + ... + mn is the total mass. In words: it is the mass-weighted average of the individual velocities. The same idea in momentum form is P = M V, so total momentum equals total mass times COM velocity.
How is the motion of the centre of mass different from the motion of one particle?
A single particle can twist and turn along any path. The COM ignores all internal complications and behaves like one simple point mass driven only by the outside force. So a spinning, wobbling system still has a COM that moves on a clean, predictable path set by F_external.
If a shell explodes in mid-air, does its centre of mass change path?
No. The explosion forces are internal, so they add to zero. The only external force is gravity, so the COM keeps following the same parabola the whole shell would have followed. The fragments scatter, but their COM stays on that original curve.
⚠️ The NEET trap ✗ Adding the speeds and thinking the COM must be moving because the particles are clearly moving fast (for example picking v or 2v as the COM speed). ✓ Check the external force first. Two particles attracting from rest have zero total momentum and no external force, so V of the COM stays exactly zero even while both particles speed up. 🧠 Fast particles do not mean a fast COM. Look at total momentum, not individual speeds.
Real NEET questions
NEET 2023 Phase 2
Two particles A and B, initially at rest, move towards each other under their mutual attraction. When A's speed is v and B's speed is 3v, the speed of the centre of mass of the system is:
A · v
B · 4v
C · 2v
D · zero ✓
Solution: Step 1: List the forces. The only force is the mutual attraction between A and B. This is an INTERNAL force, so the net external force on the system is zero.
Step 2: Apply momentum. Total momentum P = M V (COM). With no external force, P is conserved.
Step 3: Use the initial state. Both start at rest, so initial P = 0. Since P stays constant, P = 0 at every later instant.
Step 4: Conclude. P = M V = 0 with M not zero means V of the centre of mass = 0. The individual speeds v and 3v never matter. Answer: zero (D).
Solved System Of Particles And Rotational Motion NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What does 'the centre of mass moves like a single particle' mean?
It means the whole system's COM obeys M A = F_external, exactly like one point mass of mass M pushed by the total outside force. All the internal pushing and pulling is invisible to the COM.
Is momentum P = M V only true for the centre of mass?
Yes. The total linear momentum of any system equals its total mass times the velocity of its centre of mass, P = M V. That is why COM velocity is so useful in collision and explosion problems.
If no external force acts, what does the centre of mass do?
It moves with constant velocity in a straight line, just like a free particle. If it started at rest, it stays at rest forever, no matter what the parts do inside.
Why does NEET love the mutual-attraction and explosion cases?
Both hide the key idea: internal forces cancel. Students see fast-moving parts and pick a non-zero answer, but the COM only responds to external force. It is a quick trap that rewards clear thinking over calculation.
How do I quickly find COM velocity in an exam?
Write V = (sum of m times v) / (total mass). If the total momentum is zero or the external force is zero, jump straight to V = constant (often zero) without adding individual speeds.
