Center of Mass - JEE Main Previous Year Questions with Solutions

eSaral Academic and Editorial Team
Summary
Center of Mass JEE Main previous year questions cover topics including momentum conservation, elastic and inelastic collisions, center of mass of solid cones, and energy loss in collisions. Questions have appeared consistently from AIEEE 2009 through JEE Main 2018. This page provides every question with a complete, step-by-step solution.

Home > JEE Main Previous Year Questions > Center of Mass — JEE Main Previous Year Questions with Solutions

JEE Main Previous Year Question of Physics with Solutions are available here. Practicing JEE Main Previous Year Papers Questions of Physics will help all the JEE aspirants in realizing the question pattern as well as help in analyzing their weak & strong areas. Get detailed Class 11th &12th Physics Notes to prepare for Boards as well as competitive exams like IIT JEE, NEET etc. eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects. Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more. Download eSaral app for free study material and video tutorials. Simulator Previous Years AIEEE/JEE Mains Questions [esquestion] Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be :- Directions : Question number 9 contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best discribes the two statements. #tag# [AIEEE - 2009] #sol# (1) [/esquestion] [esquestion] Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions. (1) Statement–1 is true, Statement–2 is false (2) Statement–1 is true, Statement–2 is true; Statement–2 is the correct explanation of Statement–1 (3) Statement–1 is true, Statement–2 is true; Statement–2 is not the correct explanation of Statement–1 (4) Statement–1 is false, Statement–2 is true #tag# [AIEEE - 2010] #sol# (2) [/esquestion] [esquestion] This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $\mathrm{f}\left(\frac{1}{2}\mathrm{mv}^{2}\right)$then$\mathrm{f}=\left(\frac{\mathrm{m}}{\mathrm{M}+\mathrm{m}}\right)$ Statement - II : Maximum energy loss occurs when the particles get stuck together as a result of the collision. (1) Statement–I is true, Statement–II is true, Statement–II is a correct explanation of Statement–I. (2) Statement–I is true, Statement–II is true, Statement–II is a not correct explanation of Statement–I. (3) Statement–I is true, Statement–II is false. (4) Statement–I is false, Statement–II is true #tag# [JEE Mains-2013] #sol# (4) Energy loss will be maximum when collision will be perfectly inelastic (By momentum) Maximum energy loss $=\mathrm{K}_{\mathrm{i}}-\mathrm{K}_{\mathrm{f}}$ $=\frac{1}{2} \mathrm{mv}^{2}-\frac{1}{2}(\mathrm{m}+\mathrm{M}) \mathrm{v}_{\mathrm{f}}^{2}$ $=\frac{1}{2} \mathrm{mv}^{2}-\frac{1}{2}(\mathrm{m}+\mathrm{M}) \frac{\mathrm{m}^{2} \mathrm{v}^{2}}{(\mathrm{m}+\mathrm{M})^{2}}$ $=\frac{1}{2} \mathrm{mv}^{2}\left[1-\frac{\mathrm{m}}{\mathrm{m}+\mathrm{M}}\right]$ $=\left(\frac{\mathrm{M}}{\mathrm{m}+\mathrm{M}}\right) \frac{1}{2} \mathrm{mv}^{2}$ statement 1 is false. [/esquestion] [esquestion] A particle of mass m moving in the x direction with speed 2u is hit by another particle of mass 2m moving in the y direction with speed u. If the collisions perfectly inelastic , the percentage loss in the energy during the collision is close to : (1) 56 % (2) 62% (3) 44% (4) 50% #tag# [JEE Mains-2015] #sol# (1) Before collison Kinetic energy $=\frac{1}{2} \mathrm{m}(2 \mathrm{v})^{2} \times \frac{1}{2} 2 \mathrm{m}(\mathrm{v})^{2}$ $=3 \mathrm{mv}^{2}$ After collison Applying momentum conservation for inelastic collision $2 \mathrm{mv} \hat{\mathrm{j}}+\mathrm{m} 2 \mathrm{v} \hat{\mathrm{i}}=3 \mathrm{m} \overrightarrow{\mathrm{v}}_{\mathrm{f}}$ $\left|\overrightarrow{\mathrm{v}}_{\mathrm{f}}\right|=\sqrt{\frac{8}{9}} \mathrm{v}$ $\mathrm{K}_{\mathrm{f}}=\frac{1}{2} \times 3 \mathrm{m} \times\left(\mathrm{v}_{\mathrm{f}}^{2}\right)=\frac{4 \mathrm{mv}^{2}}{3}$ $\% \Delta \mathrm{K}=\frac{\mathrm{K}_{1}-\mathrm{K}_{\mathrm{f}}}{\mathrm{K}_{\mathrm{i}}} \times 100=\frac{5 \mathrm{mv}^{2} / 3}{3 \mathrm{mv}^{2}} \times 100=\frac{5}{9} \times 100=56 \%$ [/esquestion] [esquestion] Distance of the centre of mass of a solid uniform cone from its vertex is $\mathrm{Z}_{0}$. If the radius of its base is R and its height is h then $\mathrm{Z}_{0}$ is equal to :- (1) $\frac{5 \mathrm{h}}{8}$ (2) $\frac{3 \mathrm{h}^{2}}{8 \mathrm{R}}$ (3) $\frac{\mathrm{h}^{2}}{4 \mathrm{R}}$ (4) $\frac{3 \mathrm{h}}{4}$ #tag# [JEE Mains-2015] #sol# (4) for solid cone c.m. is $\frac{\mathrm{h}}{4}$ from base so $\mathrm{z}_{0}=\mathrm{h}-\frac{\mathrm{h}}{4}=\frac{3 \mathrm{h}}{4}$ [/esquestion] [esquestion] It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $\mathrm{P}_{\mathrm{d}}$ ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $\mathrm{P}_{\mathrm{c}}$. The values of $\mathrm{P}_{\mathrm{d}}$ and $\mathrm{P}_{\mathrm{c}}$ are respectively : (1) (.28, .89) (2) (0, 0) (3) (0, 1) (4) (.89, .28) #tag# [JEE Mains-2018] #sol# (4) Let initial speed of neutron is $\mathrm{v}_{0}$ and kinetic energy is K. 1st collision : by momentum conservation $\mathrm{mv}_{0}=\mathrm{mv}_{1}+2 \mathrm{mv}_{2} \Rightarrow \mathrm{v}_{1}+2 \mathrm{v}_{2}=\mathrm{v}_{0}$ by $\mathrm{e}=1 \quad \mathrm{v}_{2}-\mathrm{v}_{1}=\mathrm{v}_{0}$ [/esquestion] [esquestion] In a collinear collision, a particle with an initial speed $\mathrm{V}_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is : (1) $\sqrt{2} \mathrm{v}_{0}$ (2)$\frac{\mathrm{v}_{0}}{2}$ (3) $\frac{\mathrm{v}_{0}}{\sqrt{2}}$ (4) $\frac{\mathrm{v}_{0}}{4}$ #tag# [JEE Mains-2018] #sol# (1) Initial [/esquestion] [/esquestion]












Centre of Mass is one chapter within the wider syllabus, and the JEE PYQ chapter wise index makes it easier to track and practise the remaining topics.
Centre of Mass is only one part of the exam — see exactly how it fits into a complete paper on our JEE Main previous year question paper page.
Frequently Asked Questions
Is Center of Mass important for JEE Advanced too?
Yes. Center of Mass is equally important for JEE Advanced, where questions are typically more conceptual and multi-step. JEE Advanced may combine COM with rotational motion, variable mass systems, or impulsive forces. Mastery of JEE Main–level problems is an essential prerequisite before attempting Advanced-level questions
What is the formula for maximum energy loss in a collision?
The maximum energy loss in a collision occurs during a perfectly inelastic collision and equals [M/(m+M)] × ½mv², where m is the moving particle's mass and M is the stationary particle's mass. This is derived using momentum conservation followed by subtracting final KE from initial KE.
How many questions appear from Center of Mass in JEE Main each year?
Center of Mass and collisions typically contribute 2–4 questions per JEE Main session. The topic is part of the Systems of Particles and Rotational Motion chapter, which NTA consistently tests across both January and April sessions. Collisions (elastic and inelastic) and momentum conservation are the most frequently tested sub-topics.
How do I calculate fractional energy loss in an elastic collision?
For an elastic collinear collision between a moving particle of mass m and a stationary particle of mass M, the fractional kinetic energy loss is 4mM/(m+M)². This formula is derived by applying both momentum conservation and e = 1. It is directly used in the neutron-deuterium and neutron-carbon JEE Main 2018 question on this page.
What is the difference between elastic and inelastic collisions for JEE?
In an elastic collision, both momentum and kinetic energy are conserved (coefficient of restitution e = 1). In a perfectly inelastic collision, momentum is conserved but maximum kinetic energy is lost and the objects stick together (e = 0). JEE Main tests both types, often using statement-based or percentage-loss formats.
What is the center of mass of a solid uniform cone?
The center of mass of a solid uniform cone lies on its axis at a distance of h/4 from the base or equivalently 3h/4 from the vertex, where h is the height of the cone. This result is independent of the base radius and is derived by integrating the mass distribution along the cone's axis.

Team eSaral
eSaral Academic and Editorial Team
Team eSaral is the collective author profile for educational content created by eSaral’s teachers and academic contributors. The team draws on expertise from IIT graduates, doctors, experienced educators and subject specialists to develop resources for JEE, NEET and school students. Our articles aim to explain concepts clearly and help students study with confidence.
Related Posts

BITSAT 2027: Registration Date, Exam Date, Syllabus, Eligibility, Pattern & Fees
BITSAT 2027 exam dates, registration timeline, eligibility criteria, exam pattern, marking scheme, syllabus and fees in one page.

BITSAT Previous Year Question Paper PDF (2017-2026)
Download BITSAT previous year question papers PDF from 2017 to 2026,session-wise. Memory-based papers,exam pattern, paper analysis and how to practise

CBSE Class 10 Date Sheet 2027: Expected Exam Dates, Release Date, Admit Card & Result Timeline
CBSE Class 10 date sheet 2027 is awaited. See the expected exam dates, release window, how to download the PDF, admit card and result timelines.

NCERT Physics Class 10 Book PDF in Hindi 2026-27 – भौतिक विज्ञान के 4 अध्याय (Free Download)
NCERT Physics Class 10 book PDF in Hindi 2026-27: download all 4 chapters (अध्याय 9–12) free, with topics and important formulas.

NCERT Biology Class 9 Book Anveshan PDF in Hindi - जीव विज्ञान कक्षा 9 पुस्तक अन्वेषण PDF
Download NCERT Biology Class 9 book PDF in Hindi chapterwise for 2026-27: Cell, Tissues, Reproduction and Diversity. Free PDFs.
-1.webp?2026-10-02T10%3A55%3A05.572Z)
Essay On Artificial Intelligence in English (100,150, 200, 250, 300, 500 Words)
This is in contrast to the natural intelligence of humans. With Artificial Intelligence, machines can perform

Essay on 78th India Independence Day in English for Student (100, 150, 200, 250, 300, 500 Words)
Read the best essays on India's Independence Day in English. Short & long essays (100, 150, 200, 250, 300, 500 words) perfect for school exams
NCERT Class 11 English Snapshots book - Free PDF download- Esaral
Download NCERT Class 11 English Snapshots book PDF for free. Get all 8 chapters, chapter-wise. Start your prep today!
NCERT Class 10 biology book pdf - Free PDF Download - eSaral
NCERT Class 10 Biology book PDF 2026-27: all 5 chapters (Life Processes to Our Environment) in English & Hindi, with CBSE syllabus, marks & practical

Essay on Global Warming in English (100,150, 200, 250, 300, 500 Words)
Global warming means the Earth is getting hotter. This happens because of things like pollution from cars and factories.
