Lesson ME1-ME2

ME1-ME2 Centres of mass of particles and composite bodies Quiz: AQA Further Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson ME1-ME2, Centres of mass of particles and composite bodies: 20 multiple choice questions for the AQA Further Maths (7367), Unit 3: Optional application 1: mechanics, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. For a system of particles with masses m_i at x-coordinates x_i, which expression gives the x-coordinate of the centre of mass?

    • Sum of m_i x_i divided by the number of particles
    • Sum of x_i divided by the number of particles
    • Sum of m_i x_i divided by sum of m_i
    • Sum of m_i divided by sum of x_i

  2. The moment of a system of particles about the y-axis is equal to which of the following?

    • The sum of the masses of the particles
    • The total mass times the x-coordinate of the centre of mass
    • The total mass divided by the x-coordinate of the centre of mass
    • The sum of the x-coordinates of the particles

  3. To find the centre of mass of a composite body made of several parts, what is the usual approach?

    • Multiply the masses of the parts together
    • Add the centres of mass of the parts together
    • Average the centres of mass of the parts
    • Combine the moments of each part about the same axis and divide by the total mass

  4. Where is the centre of mass of a uniform rod?

    • At one quarter of the length from one end
    • Closer to the heavier end
    • At its midpoint
    • At one end of the rod

  5. Can the centre of mass of a body lie outside the body itself?

    • Only if the body is a single particle
    • No, the centre of mass always lies within the body
    • Yes, for example for a uniform ring with a section removed
    • Only if the body has no symmetry

  6. For a system of particles all of equal mass, what is the x-coordinate of the centre of mass?

    • The sum of the x-coordinates
    • The product of the x-coordinates
    • The largest x-coordinate
    • The arithmetic mean of the x-coordinates

  7. Where does the centre of mass of a uniform symmetric lamina lie?

    • On the boundary of the lamina
    • On the axis of symmetry
    • At the vertex of the lamina
    • At the origin always

  8. A 2 kg particle is at x = 1 m and a 3 kg particle is at x = 4 m. What is the x-coordinate of the centre of mass?

    • 2.8 m
    • 3 m
    • 2.5 m
    • 2.2 m

  9. Particles of masses 1 kg, 2 kg and 3 kg are at x = 0 m, x = 3 m and x = 6 m. What is the x-coordinate of the centre of mass?

    • 5 m
    • 4.5 m
    • 4 m
    • 3 m

  10. Particles of mass 2 kg at (1, 2), 2 kg at (3, 0) and 4 kg at (2, 4) are given. What is the position of the centre of mass?

    • (2, 2)
    • (2, 2.5)
    • (2.5, 2)
    • (3, 2.5)

  11. A 4 kg particle is at the origin and a 6 kg particle is at x = 2.5 m. What is the x-coordinate of the centre of mass of the two particles?

    • 1.75 m
    • 1.5 m
    • 1.25 m
    • 2.5 m

  12. A composite lamina has part A of mass 3 kg with centre of mass at (1, 1) and part B of mass 1 kg with centre of mass at (4, 3). What is the centre of mass of the whole lamina?

    • (2.5, 2)
    • (1.75, 1.5)
    • (2, 1.5)
    • (1.5, 1.75)

  13. A 3 kg particle is at x = 0 and an unknown mass m is at x = 5 m. The centre of mass of the system is at x = 2 m. What is m?

    • 2 kg
    • 4 kg
    • 3 kg
    • 1 kg

  14. A 5 kg particle is at the origin and a 5 kg particle is at (6, 8). What is the position of the centre of mass?

    • (3, 4)
    • (3, 8)
    • (2.5, 4)
    • (6, 8)

  15. A uniform rod of mass 2 kg and length 4 m has a 2 kg particle attached at one end. The rod centre is at its midpoint. How far is the centre of mass from the particle?

    • 2 m
    • 0.5 m
    • 1.5 m
    • 1 m

  16. A uniform square lamina of side 4 has a square of side 2 removed from one corner. What is the x-coordinate of the centre of mass of the remaining lamina, measured along the side from the corner where the square was removed?

    • 5/2 m
    • 2 m
    • 8/3 m
    • 7/3 m

  17. Particles of mass 1 kg at (0, 0), 2 kg at (3, 0) and 3 kg at (0, 6) are given. What is the centre of mass of the system?

    • (3, 1)
    • (1.5, 2.5)
    • (2, 3)
    • (1, 3)

  18. A system of total mass 8 kg has centre of mass at x = 3 m. A 2 kg particle at x = 2 m is moved to x = 6 m. What is the new x-coordinate of the centre of mass?

    • 4 m
    • 3 m
    • 5 m
    • 4.5 m

  19. Particles of mass 2 kg, 3 kg and 5 kg are at x = 1 m, x = 2 m and x = k m. The centre of mass is at x = 2.5 m. What is k?

    • 3.4
    • 3.6
    • 3
    • 3.2

  20. An L-shaped uniform lamina is formed from a rectangle [0, 4] by [0, 1] and a rectangle [0, 1] by [1, 4], each of unit density. What is the centre of mass of the lamina?

    • (19/14, 19/14)
    • (1.5, 1.5)
    • (19/7, 19/7)
    • (2, 2)

All AQA Further Maths quizzes