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Centre of Mass is a short chapter that pays well. Once you accept that a whole system can be replaced by a single point, questions on explosions, collisions and recoil become one line of arithmetic instead of a page of work. The one idea to hold on to is this: internal forces, however violent, can never move the centre of mass. Ten questions below. Give them ten honest minutes.
What this chapter carries in NEET(UG)
- Usually 2 to 3 questions every year, which is 8 to 12 marks.
- Collisions and the coefficient of restitution come up almost every year.
- The standard centre-of-mass positions for a ring, a disc and a hemisphere are asked directly.
What the syllabus says
In the syllabus (Unit 5, Rotational Motion): Centre of mass of a two-particle system, centre of mass of a rigid body.
Taken from the NMC syllabus for NEET (UG) 2026, the latest one published. See the full syllabus, unit by unit.
Formulas you must know by heart
| Centre of mass of two particles | xcm = (m1x1 + m2x2) / (m1 + m2) |
| Velocity of the centre of mass | vcm = (m1v1 + m2v2) / (m1 + m2) |
| Momentum of the system | p = M vcm |
| Semicircular ring | 2R / π from the centre |
| Semicircular disc | 4R / 3π from the centre |
| Solid hemisphere | 3R / 8 from the centre |
| Hollow hemisphere | R / 2 from the centre |
| Coefficient of restitution | e = speed of separation / speed of approach |
| Elastic collision, equal masses | the two velocities are simply exchanged |
| Perfectly inelastic collision | e = 0, the bodies move off together |
The four standard positions in the middle of that table are worth memorising as they stand. NEET(UG) asks them straight, with no working in between, and a student who knows them answers in five seconds.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. Two particles of mass 2 kg and 3 kg lie at x = 0 and x = 5 m. Their centre of mass is at
- (a) 2.0 m
- (b) 2.5 m
- (c) 3.0 m
- (d) 3.5 m
Q2. The centre of mass of a uniform semicircular ring of radius R lies at a distance from the centre of
- (a) R/2
- (b) 2R/π
- (c) 4R/3π
- (d) R/π
Q3. The centre of mass of a uniform solid hemisphere of radius R lies at a distance from the flat face of
- (a) 3R/8
- (b) 2R/π
- (c) 4R/3π
- (d) R/2
Q4. A shell at rest explodes into two pieces. If one piece carries momentum p, the other carries
- (a) p
- (b) −p
- (c) 2p
- (d) zero
Q5. A body makes a perfectly elastic head-on collision with another body of equal mass that is at rest. After the collision
- (a) they move off together
- (b) their velocities are exchanged
- (c) both come to rest
- (d) the first one rebounds with the same speed
Q6. For a perfectly inelastic collision, the coefficient of restitution is
- (a) 1
- (b) 0
- (c) 0.5
- (d) infinite
Q7. A ball dropped from a height h rebounds to a height h/4. The coefficient of restitution is
- (a) 1/4
- (b) 1/2
- (c) 1/√2
- (d) 3/4
Q8. If no external force acts on a system of particles, its centre of mass
- (a) is always at rest
- (b) moves with constant velocity
- (c) moves with constant acceleration
- (d) moves in a circle
Q9. Two particles of mass m and 2m move towards each other with speeds 2v and v. The speed of their centre of mass is
- (a) zero
- (b) v/3
- (c) v
- (d) 2v
Q10. A bomb of mass 3m at rest explodes into three equal pieces. Two of them fly off at right angles to each other, each with speed v. The speed of the third piece is
- (a) v
- (b) √2 v
- (c) 2v
- (d) v/√2
Answer key, with a hint for each
| Q1 | (c) | (2 × 0 + 3 × 5) / 5 = 3 m. The centre of mass always leans towards the heavier particle. |
| Q2 | (b) | A standard result. Keep ring 2R/π, disc 4R/3π, solid hemisphere 3R/8 together in one line of memory. |
| Q3 | (a) | Solid hemisphere is 3R/8. The hollow one is R/2, which is the usual trap in this question. |
| Q4 | (b) | Total momentum was zero before, so it must stay zero. The two pieces carry equal and opposite momentum. |
| Q5 | (b) | For equal masses in an elastic head-on collision, the moving one stops dead and the still one moves off with its speed. |
| Q6 | (b) | Perfectly inelastic means they do not separate at all, so the speed of separation is zero. |
| Q7 | (b) | e = √(h′/h) = √(1/4). |
| Q8 | (b) | Zero external force means zero acceleration of the centre of mass, not zero velocity. It keeps whatever velocity it had. |
| Q9 | (a) | They approach each other, so the momenta are opposite: m(2v) one way and 2m(v) the other. They cancel. |
| Q10 | (b) | The two known pieces carry momentum mv each at right angles, so together √2 mv. The third must carry the same amount the other way. |
Now mark yourself honestly
NEET(UG) marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 45 Physics questions are out of 180.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in May.
The full chapter, on a clock
Ten questions tell you a little. Forty-five tell you the truth.
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