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Centre of Mass for JEE: 41 solved questions

Real JEE paper questions on centre of mass, part of rotational motion. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2002 to 2026. No sign-in needed to read them.

What this topic asks

• Centre of mass by integration — 10 questions
• Discrete systems and motion of the centre of mass — 7 questions
• Centre of mass of a non-uniform rod — 4 questions
• Centre of mass of a body with a cavity — 2 questions
• Keeping the centre of mass fixed — 2 questions
• Centre of mass of point masses — 2 questions
• Centre of mass of a system in motion — 1 question
• Motion of the centre of mass — 1 question
• Kinetic energy of a system of particles — 1 question
• Centre of mass of a composite lamina — 1 question
• Centre of mass and internal work — 1 question
• Explosion and the centre of mass — 1 question
• Centre of mass of a composite body — 1 question
• Centre of mass under internal forces — 1 question
• Centre of mass of a lamina with a notch — 1 question
• Centre of mass of a semicircular wire — 1 question
• Velocity of the centre of mass — 1 question
• Centre of mass of a quarter disc — 1 question
• Centre of mass of a solid hemisphere — 1 question
• Acceleration of the centre of mass — 1 question

All 41 questions with solutions

• Three masses 2 kg, 3 kg and 15 kg are placed as shown: 2 kg and 3 kg at the two base corners and 15 kg at the… JEE Main 6th April 1st Shift 2026
• A thin rod of length 5L is bent at a right angle keeping one arm of length 2L (along y) and the other of leng… JEE Main 7th April 1st Shift 2025
• A circular disc of radius 20 cm is centred at the origin. A circular hole of radius 5 cm is cut such that the… JEE Main 23rd Jan 1st Shift 2025
• The centre of mass of a thin rectangular plate (sides a along x and b along y), whose mass per unit area vari… JEE Main 28th Jan 1st Shift 2025
• Two bodies of mass 1 kg and 3 kg have position vectors ̂i+2̂j+̂k and -3̂i-2̂j+̂k respectively. The magnitude… JEE Main 29th July 1st Shift 2022
• Two blocks of masses 10 kg and 30 kg are placed on a straight line with coordinates (0,0) cm and (x,0) cm. Th… JEE Main 27th June 1st Shift 2022
• A circular hole of radius a/2 is cut out of a circular disc of radius a, so that the hole's centre is at a/2… JEE Main 24th Feb 2nd Shift 2021
• Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right-angle triang… JEE Main 7th Jan 1st Shift 2020
• A rod of length L has a non-uniform linear mass density ρ(x)=a+b(x/L)², with 0≤ x≤ L. The value of x for the… JEE Main 7th Jan 2nd Shift 2020
• A spherical cavity of radius 1 (centred at O) is cut out of a uniform solid sphere of radius R (centred at C)… JEE Main 8th Jan 2nd Shift 2020
• A uniform rectangular thin sheet ABCD of mass M has length a and breadth b. If the top-right quarter (HBGO, w… JEE Main 8th April 2nd Shift 2019
• Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side… JEE Main 12th April 2nd Shift 2019
• The position vector of the centre of mass of an asymmetric uniform bar (negligible cross-section) is, for the… JEE Main 12th Jan 1st Shift 2019
• ABC is a uniform wire bent so that the angle at B is 60°. If the centre of mass of the wire lies vertically b… JEE Main Online 2016
• The distance of the centre of mass of a solid uniform cone from its vertex is z₀. If the base radius is R and… JEE Main 2015
• A projectile of mass M is fired so that its horizontal range is 4 km. At the highest point it explodes into t… JEE Main Online 2013
• Two identical particles move towards each other with velocities 2v and v respectively. The velocity of the ce… AIEEE 2002
• Two blocks of masses 2 kg and 1 kg are tied to the ends of a string passing over a light frictionless pulley.… JEE Main 2nd April 2nd Shift 2026
• Two identical bodies A and B of equal masses have initial velocities ⃗v₁=4̂i m/s and ⃗v₂=4̂j m/s respectively… JEE Main 6th April 2nd Shift 2026
• Given below are two statements: Statement I: For a mechanical system of many particles, the total kinetic ene… JEE Main 22nd Jan 2nd Shift 2026
• The coordinates of the centre of mass of a uniform flag-shaped lamina (a thin flat plate) of mass 4 kg are (t… JEE Main 8th Jan 1st Shift 2020
• A person of mass M is sitting on a swing of length L and swinging with an angular amplitude θ₀. If the person… JEE Main 12th April 1st Shift 2019
• A uniform thin rod AB of length L has linear mass density μ(x)=a+(bx)/L, where x is measured from A. If the c… JEE Main Online 2015
• A thin bar of length L has a mass per unit length λ that increases linearly with distance from one end. If it… JEE Main Online 2014
• A projectile moving vertically upwards with a velocity of 200 m s⁻¹ breaks into two equal parts at a height o… JEE Main Online 2012
• A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences… JEE Main 2007
• Consider a two-particle system with particles having masses m₁ and m₂. If the first particle is pushed toward… JEE Main 2006
• A T-shaped object with dimensions shown in the figure is lying on a smooth floor. A force ⃗F is applied at th… JEE Main 2005
• A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1… JEE Main 2005
• In a system two particles of masses m₁=3 kg and m₂=2 kg are placed at a certain distance from each other. The… JEE Main 4th April 2nd Shift 2024
• A uniform thin metal plate of mass 10 kg with the dimensions shown has the ratio of the x and y coordinates o… JEE Main 8th April 1st Shift 2024
• Three identical spheres each of mass 2M are placed at the corners of a right-angled triangle with mutually pe… JEE Main 1st Feb 1st Shift 2024
• Three identical spheres each of mass M are placed at the corners of a right-angled triangle with mutually per… JEE Main 25th July 2nd Shift 2022
• The distance of the centre of mass from end A of a one-dimensional rod AB having mass density ρ=ρ₀(1-(x²)/(L²… JEE Main 28th July 2nd Shift 2022
• The position of the centre of mass of a uniform semicircular wire of radius R placed in the x-y plane with it… JEE Main 22nd July 2nd Shift 2021
• A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and con… JEE Main 25th July 1st Shift 2021
• A disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarte… JEE Main 17th March 2nd Shift 2021
• A square-shaped hole of side l=a/2 is carved out at a distance d=a/2 from the centre O of a uniform circular… JEE Main 2nd Sept 2nd Shift 2020
• The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then the… JEE Main 6th Sept 2nd Shift 2020
• Four particles A, B, C and D with masses m_A=m, m_B=2m, m_C=3m and m_D=4m are at the corners of a square, as… JEE Main 8th April 1st Shift 2019
• A thin rod of length L is lying along the x-axis with its ends at x=0 and x=L. Its linear density (mass/lengt… JEE Main 2008