Sit a full JEE Main paper, free
25 questions, 45 minutes, out of 100, marked the way the exam marks it. No payment, no card, and no account needed to start.
1,000 XP coins free the first time you open your portal — enough to open a whole chapter level there and then.
Centre of Mass is a small chapter that JEE Main uses to test whether you really trust conservation of momentum. Two blocks and a spring, a person walking on a boat, a disc with a hole cut out — every one of them is solved by the same sentence: no external force, so the centre of mass does not move. Say that to yourself before you start writing. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 1 to 2 questions every year, which is 4 to 8 marks.
- Collisions and the loss of kinetic energy are the regular ones.
- Centre of mass shifts and cavity problems come up often.
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 NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Centre of mass | xcm = Σmx / Σm |
| Momentum of the system | p = M vcm |
| Triangular lamina | at h/3 from the base |
| Semicircular ring and disc | 2R/π and 4R/3π |
| Solid and hollow hemisphere | 3R/8 and R/2 |
| Elastic collision, first body | v1′ = (m1 − m2)u1/(m1 + m2) |
| Elastic collision, second body | v2′ = 2m1u1/(m1 + m2) |
| Loss of energy, perfectly inelastic | ΔKE = m1m2(u1 − u2)2 / 2(m1 + m2) |
| Coefficient of restitution | e = speed of separation / speed of approach |
| Cavity cut out of a body | shift = m′d / (M − m′) |
The loss-of-energy formula has the relative velocity in it, not the individual speeds. That is the whole point: a collision only destroys the energy of the approach, and whatever the two bodies share as a common motion survives untouched.
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. Particles of mass 1 kg, 2 kg and 3 kg lie at (0, 0), (1, 0) and (0, 1). The x coordinate of their centre of mass is
- (a) 1/3
- (b) 1/2
- (c) 2/3
- (d) 1
Q2. Two blocks of mass m and 2m are pushed apart by a compressed spring on a frictionless floor. The ratio of their speeds is
- (a) 1 : 2
- (b) 2 : 1
- (c) 1 : 1
- (d) 4 : 1
Q3. A person of 60 kg walks from one end to the other of a 120 kg boat of length 3 m floating freely. The boat moves through
- (a) 0.5 m
- (b) 1 m
- (c) 1.5 m
- (d) 2 m
Q4. The centre of mass of a uniform triangular lamina lies at a height above the base of
- (a) h/2
- (b) h/3
- (c) 2h/3
- (d) h/4
Q5. A 1 kg body moving at 4 m/s strikes a stationary 3 kg body and they move off together. Their common speed is
- (a) 1 m/s
- (b) 2 m/s
- (c) 3 m/s
- (d) 4 m/s
Q6. In the collision just described, the kinetic energy lost is
- (a) 2 J
- (b) 4 J
- (c) 6 J
- (d) 8 J
Q7. A particle of mass m moving with speed v collides elastically and head-on with a stationary particle of mass 3m. After the collision the first particle moves
- (a) forward at v/2
- (b) backward at v/2
- (c) forward at v
- (d) not at all
Q8. A disc of radius R has a circular hole of radius R/2 cut out, the hole touching the rim. The centre of mass of what is left shifts from the centre by
- (a) R/2
- (b) R/4
- (c) R/6
- (d) R/3
Q9. The centre of mass of a system moves exactly as though
- (a) the internal forces acted at that point
- (b) all the mass were there and all the external forces acted there
- (c) it were permanently at rest
- (d) no force acted on the system
Q10. For a perfectly elastic collision, the coefficient of restitution is
- (a) 0
- (b) 0.5
- (c) 1
- (d) infinite
Answer key, with a hint for each
| Q1 | (a) | (1×0 + 2×1 + 3×0)/6 = 2/6. |
| Q2 | (b) | Total momentum stays zero, so mv1 = 2mv2. The lighter block moves twice as fast. |
| Q3 | (b) | The centre of mass cannot move, so the boat slides back by mL/(M + m) = 60 × 3 / 180. |
| Q4 | (b) | The centroid, which sits one third of the way up from the base. |
| Q5 | (a) | Momentum 1 × 4 = 4 is shared by 4 kg, giving 1 m/s. |
| Q6 | (c) | Before 8 J, after ½ × 4 × 1 = 2 J. |
| Q7 | (b) | v1′ = (m − 3m)v/(4m) = −v/2. A light body always bounces back off a heavier one. |
| Q8 | (c) | The cut-out mass is M/4 and its centre is R/2 from the centre, so the shift is (M/4 × R/2)/(3M/4), away from the hole. |
| Q9 | (b) | Internal forces never move it, however violent they are. |
| Q10 | (c) | Elastic means the bodies separate exactly as fast as they approached. |
Now mark yourself honestly
JEE Main 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, 25 Physics questions are out of 100.
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 January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
The Foundation paper for Centre of Mass and System of Particles is waiting for you on the portal: 25 questions, 45 minutes, marked out of 100, with the answer key and a hint for every question. Sit it tonight and you will know exactly where this chapter stands.
Free the moment you register
1,000 XP coins, free
A Foundation paper opens for 230 coins, so your first four are already paid for. And every paper you sit sincerely pays you more.
Every chapter of JEE Main Physics has three papers on the portal: Foundation, Intermediate and Expert. You move up only when you clear the one below. 30 chapters, 90 papers, open 24×7.
Want to know how many marks this chapter usually carries? See the JEE Main Physics chapter-wise weightage.
All the formulas for every chapter in one place: JEE Main Physics formula sheet.
One JEE Main Physics question every morning
It comes at 7 AM on Telegram. Tap the option you think is right and you will know at once whether it was. The worked hint follows the next morning.