JEE Main · Physics · System of Particles and Rotational Motion
Center of Mass: JEE Main previous year questions
25 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 7 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 25
- in 25 of 108 shifts
- Years asked
- 6/8
- last asked 2026
- Weighted estimate
- 0.2
- model; history: 0.2 a shift on average, typically 0.0–0.3
Key findings
- 01
Asked in 6 of 8 years with analysed shifts and in 25 of 108 shifts: 25 questions, #123 of 196 topics. The years that asked it were 1.2 apart on average.
- 02
68% of its questions since 2020 tested an idea no earlier year had asked; 4 repeated an idea from the year before.
- 03
The most repeated idea is Discrete System COM, asked 5 times in 5 shifts (2022, 2024, 2026), most often as “centre of mass of three-point-mass system”.
- 04
JEE Main has asked 13 of the 51 ideas in this topic; 35 have never been asked, directly or inside another question.
- 05
Mostly asked as numerical value (48%); 48% need a numerical answer, 56% are easy and 4% hard.
- 06
The skill tested most is calculation (68%), then application (16%).
Questions a shift, year by year
Out of the 25 Physics questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 5 in 12 shifts · 2021: 6 in 24 shifts · 2022: 7 in 24 shifts · 2023: 0 in 12 shifts · 2024: 3 in 18 shifts · 2025: 1 in 8 shifts · 2026: 3 in 9 shifts.
- Up to 2023
- 0.2
- a shift, of 25
- Since 2024
- 0.2
- 0.0
- Usual gap
- 1.2 yrs
- between years asking it
- Shifts with it
- 25/108
- 23% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 25 questions on Center of Mass since 2017.
Difficulty
QUESTIONS- Easy14 · 56%
- Medium10 · 40%
- Hard1 · 4%
Format
SHARE- Numerical value · 12 Q48%
- Single correct · 11 Q44%
- Diagram based · 2 Q8%
Skill tested
SHARE- Calculation · 17 Q68%
- Application · 4 Q16%
- Multi-step · 3 Q12%
- Recall · 1 Q4%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 13 of the 51 ideas in this topic. 35 have never been asked yet.
- Asked directly13 · 25%
- Touched inside another question3 · 6%
- Never asked35 · 69%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
11 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
13 different ideas were tested; 5 came more than once.
centre of mass of three-point-mass system
Single correct · 5 shifts · 2 numericalcentre of mass speed after elastic collision
Numerical value · 4 shifts · 3 numericalcentre of mass of plate with cutout
Diagram based · 3 shifts · 1 numericalcentre of mass of disc with circular hole
Diagram based · 3 shifts · 1 numericalcentre of mass of rod with variable density
Numerical value · 2 shifts · 1 numericaldisplacement of centre of mass in atwood machine
Single correct · 1 shiftidentify path of centre of mass from vectors
Single correct · 1 shiftcentre of mass of bent rod
Single correct · 1 shiftdisplacement of second particle to keep centre of mass fixed
Numerical value · 1 shift · 1 numericalmaximum spring elongation for two blocks given opposite velocities
Single correct · 1 shiftcentre of mass of semicircular wire
Numerical value · 1 shift · 1 numericalcentre of mass of quarter disc
Numerical value · 1 shift · 1 numericalcentre of mass of solid hemisphere
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Discrete System COMcentre of mass of three-point-mass system | 5 | 5 | Single correctCalculation | 2 | |
| COM Velocity Conservationcentre of mass speed after elastic collision | 4 | 4 | Numerical valueCalculation | 3 | |
| COM of Composite Bodiescentre of mass of plate with cutout | 3 | 3 | Diagram basedCalculation | 1 | |
| COM of Cavity Bodiescentre of mass of disc with circular hole | 3 | 3 | Diagram basedApplication | 1 | |
| COM of Non-Uniform Rodcentre of mass of rod with variable density | 2 | 2 | Numerical valueCalculation | 1 | |
| COM Acceleration in Atwood Machinedisplacement of centre of mass in atwood machine | 1 | 1 | Single correctMulti-step | – | |
| Vector Kinematics of COMidentify path of centre of mass from vectors | 1 | 1 | Single correctApplication | – | |
| COM of Bent Wirescentre of mass of bent rod | 1 | 1 | Single correctCalculation | – | |
| Internal Mass Displacementdisplacement of second particle to keep centre of mass fixed | 1 | 1 | Numerical valueCalculation | 1 | |
| COM of Two-Block Spring Systemmaximum spring elongation for two blocks given opposite velocities | 1 | 1 | Single correctApplication | – | |
| COM of Circular Arccentre of mass of semicircular wire | 1 | 1 | Numerical valueCalculation | 1 | |
| COM of Circular Sectorcentre of mass of quarter disc | 1 | 1 | Numerical valueApplication | 1 | |
| COM of Hemispherical Bodiescentre of mass of solid hemisphere | 1 | 1 | Numerical valueRecall | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Center of Mass questions, year by year
The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.
JEE Main 20263 questions in 3 shifts
- 2 Apr, Shift 2Q28Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown…
Idea: COM Acceleration in Atwood Machine
New ideaMediumSingle correct · figure - 6 Apr, Shift 1Q33The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point () of normal bisector, as shown in…
Idea: Discrete System COM
EasySingle correct · figure - 6 Apr, Shift 2Q32Two identical bodies A and B of equal masses have initial velocities m/s and m/s respectively.…
Idea: Vector Kinematics of COM
New ideaMediumSingle correct
JEE Main 20251 question in 1 shift
- 7 Apr, Shift 1Q29A rod of length 5 L is bent right angle keeping one side length as 2 L. The position of the centre of mass of the system: (Consider L = 10…
Idea: COM of Bent Wires
New ideaEasySingle correct · figure
JEE Main 20243 questions in 3 shifts
- 4 Apr, Shift 2Q58In a system two particles of masses = 3 and = 2 are placed at certain distance from each other. The particle of mass…
Idea: Internal Mass Displacement
New ideaEasyNumerical value - 8 Apr, Shift 1Q52A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of and coordinates of center of mass of plate in…
Idea: COM of Composite Bodies
MediumNumerical value · figure - 1 Feb, Shift 1Q52The identical spheres each of mass 2M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m…
Idea: Discrete System COM
EasyNumerical value
JEE Main 20227 questions in 7 shifts
- 25 Jul, Shift 2Q52Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m…
Idea: Discrete System COM
New ideaEasyNumerical value - 26 Jul, Shift 1Q47As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant . If both are…
Idea: COM of Two-Block Spring System
New ideaMediumSingle correct · figure - 28 Jul, Shift 2Q22The distance of centre of mass from end A of a one dimensional rod (AB) having mass density …
Idea: COM of Non-Uniform Rod
MediumNumerical value - 29 Jul, Shift 1Q36Two bodies of mass 1 kg and 3 kg have position vectors and respectively.…
Idea: Discrete System COM
New ideaEasySingle correct - 30 Jul, Shift 2Q3A bullet of mass 10 gram is fired with velocity of 100 m/s from the gun of mass 1 kg . Recoil speed of the gun is :
Idea: COM Velocity Conservation
Asked the year beforeEasySingle correct - 27 Jun, Shift 1Q35Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates cm and cm respectively. The…
Idea: Discrete System COM
New ideaEasySingle correct - 28 Jun, Shift 1Q56A man of 60 kg is running on the road and suddenly jumps into a stationary trolley car of mass 120 kg. Then, the trolley car starts moving…
Idea: COM Velocity Conservation
Asked the year beforeEasyNumerical value
JEE Main 20216 questions in 6 shifts
- 4 Aug, Shift 1Q13Choose the correct option for the centre of mass of a uniform disc of radius ‘R’ from which a circular section of radius r (2r < R) has…
Idea: COM of Cavity Bodies
Asked the year beforeMediumSingle correct - 31 Aug, Shift 1Q24A block moving horizontally on a smooth surface with a speed of 40 ms splits into two equal parts. If one of the parts moves at 60…
Idea: COM Velocity Conservation
New ideaEasyNumerical value - 24 Feb, Shift 2Q3A circular hole of radius is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the…
Idea: COM of Composite Bodies
Asked the year beforeMediumDiagram based · figure - 22 Jul, Shift 2Q22The position of the centre of mass of a uniform semi-circular wire of radius ‘R’ placed in - plane with its centre at the origin and…
Idea: COM of Circular Arc
New ideaEasyNumerical value - 25 Jul, Shift 1Q21A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the…
Idea: COM Velocity Conservation
New ideaMediumNumerical value - 17 Mar, Shift 2Q27The disc of mass M with uniform surface mass density is shown in the figure. The centre of mass of the quarter disc (the shaded…
Idea: COM of Circular Sector
New ideaMediumNumerical value · figure
JEE Main 20205 questions in 5 shifts
- 8 Jan, Shift 1Q3The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg. (The coordinates of the same are shown…
Idea: COM of Composite Bodies
New ideaEasySingle correct · figure - 8 Jan, Shift 2Q4As shown in fig. when a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre…
Idea: COM of Cavity Bodies
New ideaHardDiagram based · figure - 9 Jan, Shift 2Q5A rod of length has non-uniform linear mass density given by , where and are…
Idea: COM of Non-Uniform Rod
New ideaEasySingle correct - 2 Sep, Shift 2Q22A square shaped hole of side is carved out at a distance from the centre ‘O’ of a uniform circular…
Idea: COM of Cavity Bodies
New ideaMediumNumerical value · figure - 6 Sep, Shift 2Q21The centre of mass of a solid hemisphere of radius 8 cm is cm from the centre of the flat surface. Then value of is ________.
Idea: COM of Hemispherical Bodies
New ideaEasyNumerical value
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.