JEE Main · Physics · System of Particles and Rotational Motion
Moment of Inertia: JEE Main previous year questions
45 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 12 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 45
- in 43 of 108 shifts
- Years asked
- 8/8
- last asked 2026
- Weighted estimate
- 0.4
- model; history: 0.5 a shift on average, typically 0.2–0.7
Key findings
- 01
Asked in 8 of 8 years with analysed shifts and in 43 of 108 shifts: 45 questions, #69 of 196 topics. It came in every year with analysed shifts.
- 02
39% of its questions since 2020 tested an idea no earlier year had asked; 15 repeated an idea from the year before.
- 03
The most repeated idea is Parallel Axis Theorem, asked 7 times in 7 shifts (2020, 2021, 2024, 2026), most often as “matching moments of inertia using parallel axis”.
- 04
JEE Main has asked 18 of the 55 ideas in this topic; 34 have never been asked, directly or inside another question.
- 05
Mostly asked as numerical value (53%); 53% need a numerical answer, 24% are easy and 13% hard.
- 06
The skill tested most is calculation (53%), then multi-step (33%).
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: 1 in 1 shift · 2020: 8 in 12 shifts · 2021: 11 in 24 shifts · 2022: 7 in 24 shifts · 2023: 6 in 12 shifts · 2024: 4 in 18 shifts · 2025: 5 in 8 shifts · 2026: 3 in 9 shifts.
- Up to 2023
- 0.5
- a shift, of 25
- Since 2024
- 0.4
- -0.1
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 43/108
- 40% of analysed shifts
Revise first
- MOI of Composite Bodies · asked 2020, 2021, 2022, 2023, 2025
- Parallel Axis Theorem · asked 2020, 2021, 2024, 2026
- MOI of Standard Shapes · asked 2020, 2021, 2022, 2023, 2026
How it is asked
Difficulty, format and skill
Across all 45 questions on Moment of Inertia since 2017.
Difficulty
QUESTIONS- Easy11 · 24%
- Medium28 · 62%
- Hard6 · 13%
Format
SHARE- Numerical value · 24 Q53%
- Single correct · 17 Q38%
- Diagram based · 2 Q4%
- Assertion–reason · 1 Q2%
- Match the list · 1 Q2%
Skill tested
SHARE- Calculation · 24 Q53%
- Multi-step · 15 Q33%
- Application · 3 Q7%
- Conceptual · 2 Q4%
- Recall · 1 Q2%
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 18 of the 55 ideas in this topic. 34 have never been asked yet.
- Asked directly18 · 33%
- Touched inside another question3 · 5%
- Never asked34 · 62%
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
Idea, year, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
- 2 Apr ’26 S2 · Q50Moment of inertia about an axis for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius…
mediumNumerical value
- 31 Jan ’24 S2 · Q52Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers…
mediumNumerical value
- 26 Aug ’21 S2 · Q10The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia…
mediumDiagram basedAsked the year before
- 27 Aug ’21 S1 · Q2Moment of inertia of a square plate of side about the axis passing through one of the corner and perpendicular to the plane of square…
easySingle correctAsked the year before
- 31 Aug ’21 S2 · Q14A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the ends of a light rod. The distance between the…
mediumSingle correctAsked the year before
- 26 Feb ’21 S1 · Q5Read the question
mediumSingle correctAsked the year before
- 4 Sep ’20 S2 · Q5Read the question
easyDiagram basedNew idea
- 2 Apr ’26 S2 · Q50
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
18 different ideas were tested; 9 came more than once.
matching moments of inertia using parallel axis
Single correct · 7 shifts · 2 numericalmoment of inertia of system of bodies about axis
Numerical value · 6 shifts · 4 numericaltorque and rotations to stop a sphere
Numerical value · 5 shifts · 4 numericalmoment of inertia of masses at triangle edge centres
Numerical value · 5 shifts · 5 numericalassertion-reason on moment of inertia
Numerical value · 5 shifts · 3 numericalratio of moments of inertia after reshaping
Numerical value · 2 shifts · 1 numericalmoment of inertia of ring formed from rod
Single correct · 2 shiftsmoment of inertia of composite system
Numerical value · 2 shifts · 1 numericalminimise moment of inertia of cylinder
Single correct · 2 shiftsmoment of inertia of ring about tangent
Single correct · 1 shiftmoment of inertia of disc with hole
Numerical value · 1 shift · 1 numericalmoment of inertia of semicircular ring about centre
Numerical value · 1 shift · 1 numericalmatch list on moment of inertia of bodies
Match the list · 1 shiftorder/ranking of moments of inertia of bodies
Single correct · 1 shiftmoment of inertia of wire bent into polygon
Numerical value · 1 shift · 1 numericalmoi of lamina with part removed
Numerical value · 1 shift · 1 numericalmoment of inertia of rod with varying density
Single correct · 1 shiftratio of moments of inertia from scaling
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Parallel Axis Theoremmatching moments of inertia using parallel axis | 7 | 7 | Single correctCalculation | 2 | |
| MOI of Composite Bodiesmoment of inertia of system of bodies about axis | 6 | 6 | Numerical valueMulti-step | 4 | |
| MOI of Standard Shapestorque and rotations to stop a sphere | 5 | 5 | Numerical valueCalculation | 4 | |
| MOI of Discrete Particlesmoment of inertia of masses at triangle edge centres | 5 | 5 | Numerical valueCalculation | 5 | |
| Radius of Gyrationassertion-reason on moment of inertia | 5 | 5 | Numerical valueCalculation | 3 | |
| MOI Changes During Reshapingratio of moments of inertia after reshaping | 2 | 2 | Numerical valueCalculation | 1 | |
| MOI Change by Bending a Rodmoment of inertia of ring formed from rod | 2 | 2 | Single correctApplication | – | |
| MOI of Spheres About a Tangentmoment of inertia of composite system | 2 | 2 | Numerical valueCalculation | 1 | |
| MOI of a Cylinder About Transverse Axisminimise moment of inertia of cylinder | 2 | 2 | Single correctMulti-step | – | |
| MOI of a Ring About Tangentsmoment of inertia of ring about tangent | 1 | 1 | Single correctApplication | – | |
| MOI of Bodies with Cavitiesmoment of inertia of disc with hole | 1 | 1 | Numerical valueCalculation | 1 | |
| MOI of Sectors and Arcsmoment of inertia of semicircular ring about centre | 1 | 1 | Numerical valueCalculation | 1 | |
| MOI of a Disk About Tangentsmatch list on moment of inertia of bodies | 1 | 1 | Match the listRecall | – | |
| Comparing MOI of Standard Shapesorder/ranking of moments of inertia of bodies | 1 | 1 | Single correctConceptual | – | |
| MOI of a Polygonal Wire Loopmoment of inertia of wire bent into polygon | 1 | 1 | Numerical valueCalculation | 1 | |
| MOI of a Triangular Platemoi of lamina with part removed | 1 | 1 | Numerical valueMulti-step | 1 | |
| MOI with Linear Density Gradientmoment of inertia of rod with varying density | 1 | 1 | Single correctCalculation | – | |
| Scaling Laws for MOIratio of moments of inertia from scaling | 1 | 1 | Single correctCalculation | – |
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
Moment of Inertia questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20263 questions in 3 shifts
- 2 Apr, Shift 2Q50Moment of inertia about an axis for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius…
Idea: Parallel Axis Theorem
MediumNumerical value · figure - 4 Apr, Shift 1Q30A solid sphere of mass and radius is divided into two unequal parts. The smaller part having mass is converted into a sphere…
Idea: MOI Changes During Reshaping
MediumSingle correct - 6 Apr, Shift 1Q31A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular…
Idea: MOI of Standard Shapes
MediumSingle correct
JEE Main 20255 questions in 5 shifts
- 2 Apr, Shift 1Q32Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is ''. Now…
Idea: MOI of Composite Bodies
MediumSingle correct - 2 Apr, Shift 2Q28The moment of inertia of a circular ring of mass and diameter about a tangential axis lying in the plane of the ring is :
Idea: MOI of a Ring About Tangents
New ideaEasySingle correct - 7 Apr, Shift 1Q46A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.…
Idea: MOI of Composite Bodies
HardNumerical value · figure - 7 Apr, Shift 2Q46and be the mass and radius of a disc. A small disc of radius is removed from the bigger disc as shown in figure. The…
Idea: MOI of Bodies with Cavities
New ideaMediumNumerical value · figure - 8 Apr, Shift 2Q28A rod of linear mass density '' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its…
Idea: MOI Change by Bending a Rod
MediumSingle correct
JEE Main 20244 questions in 4 shifts
- 5 Apr, Shift 1Q35Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis…
Idea: Radius of Gyration
Asked the year beforeMediumSingle correct · figure - 6 Apr, Shift 2Q56Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m. The…
Idea: MOI of Discrete Particles
MediumNumerical value - 27 Jan, Shift 1Q52Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis…
Idea: MOI of Discrete Particles
EasyNumerical value - 31 Jan, Shift 2Q52Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers…
Idea: Parallel Axis Theorem
MediumNumerical value
JEE Main 20236 questions in 6 shifts
- 6 Apr, Shift 1Q60Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of…
Idea: MOI of Composite Bodies
Asked the year beforeMediumNumerical value - 6 Apr, Shift 2Q52A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is…
Idea: Radius of Gyration
Asked the year beforeMediumNumerical value - 8 Apr, Shift 1Q53The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is…
Idea: MOI of Sectors and Arcs
New ideaEasyNumerical value - 11 Apr, Shift 1Q58A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s. If the moment of…
Idea: MOI of Spheres About a Tangent
MediumNumerical value - 12 Apr, Shift 1Q53For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is . The value of is ______
Idea: MOI of Standard Shapes
Asked the year beforeMediumNumerical value - 15 Apr, Shift 1Q53A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their…
Idea: Radius of Gyration
Asked the year beforeEasyNumerical value
JEE Main 20227 questions in 7 shifts
- 26 Jul, Shift 1Q52A disc of mass 1 kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of…
Idea: MOI of Discrete Particles
HardNumerical value - 26 Jul, Shift 2Q52The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be…
Idea: Radius of Gyration
Asked the year beforeEasyNumerical value - 28 Jul, Shift 1Q60Four identical discs each of mass 'M' and diameter 'a' are arranged in a small plane as shown in figure. If the moment of inertia of the…
Idea: MOI of Composite Bodies
Asked the year beforeMediumNumerical value · figure - 25 Jun, Shift 2Q54Moment of Inertia (M.I.) of four bodies having same mass ‘’ and radius ‘’ are as follows : = M.I. of solid sphere…
Idea: MOI of Standard Shapes
Asked the year beforeMediumNumerical value - 28 Jun, Shift 1Q34Match List-I with List-II List - I | List - II A. Moment of inertia of solid sphere of radius R about any tangent. | I. …
Idea: MOI of a Disk About Tangents
New ideaMediumMatch the list - 29 Jun, Shift 2Q57The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is . The same rod is bent into a ring…
Idea: MOI Changes During Reshaping
New ideaMediumNumerical value - 30 Jun, Shift 1Q53Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure).…
Idea: MOI of Discrete Particles
EasyNumerical value · figure
JEE Main 202111 questions in 11 shifts
- 3 Aug, Shift 2Q4A solid sphere of radius has mass . A rod of mass is attached tangentially to the sphere. What would be the moment of inertia…
Idea: MOI of Spheres About a Tangent
New ideaMediumSingle correct - 26 Aug, Shift 1Q22Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton…
Idea: MOI of Composite Bodies
Asked the year beforeHardNumerical value · figure - 26 Aug, Shift 2Q10The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia…
Idea: Parallel Axis Theorem
Asked the year beforeMediumDiagram based · figure - 27 Aug, Shift 1Q2Moment of inertia of a square plate of side about the axis passing through one of the corner and perpendicular to the plane of square…
Idea: Parallel Axis Theorem
Asked the year beforeEasySingle correct - 31 Aug, Shift 2Q14A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the ends of a light rod. The distance between the…
Idea: Parallel Axis Theorem
Asked the year beforeMediumSingle correct - 24 Feb, Shift 1Q4Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as ; = M.I. of thin circular ring about its…
Idea: Comparing MOI of Standard Shapes
New ideaMediumSingle correct - 24 Feb, Shift 2Q23A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing…
Idea: MOI of a Polygonal Wire Loop
New ideaMediumNumerical value - 26 Feb, Shift 1Q5Four identical solid spheres each of mass ‘m’ and radius ‘a’ are placed with their centres on the four corners of a square of side ‘b’.…
Idea: Parallel Axis Theorem
Asked the year beforeMediumSingle correct - 25 Jul, Shift 1Q15Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Moment of inertia of…
Idea: Radius of Gyration
New ideaEasyAssertion–reason - 25 Jul, Shift 2Q22A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane…
Idea: MOI of Standard Shapes
Asked the year beforeEasyNumerical value - 18 Mar, Shift 2Q6Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the…
Idea: MOI Change by Bending a Rod
New ideaEasySingle correct
JEE Main 20208 questions in 6 shifts
- 9 Jan, Shift 1Q4Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral…
Idea: MOI of Composite Bodies
New ideaMediumSingle correct · figure - 9 Jan, Shift 1Q22One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest when it makes an angle …
Idea: MOI of Standard Shapes
New ideaMediumNumerical value · figure - 3 Sep, Shift 1Q4Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of…
Idea: MOI of a Cylinder About Transverse Axis
Asked the year beforeHardSingle correct - 3 Sep, Shift 2Q22An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass m situated at its vertices. The moment…
Idea: MOI of Discrete Particles
New ideaMediumNumerical value · figure - 4 Sep, Shift 1 · Q21MOI of a Triangular PlateNew ideaHard
- 4 Sep, Shift 2 · Q4Scaling Laws for MOINew ideaMedium
- 4 Sep, Shift 2 · Q5Parallel Axis TheoremNew ideaEasy
- 6 Sep, Shift 2 · Q5MOI with Linear Density GradientNew ideaMedium
JEE Main 20171 question in 1 shift
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.