Lesson ME3-ME4

ME3-ME4 Centres of mass of laminas and solids of revolution Quiz: AQA Further Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson ME3-ME4, Centres of mass of laminas and solids of revolution: 20 multiple choice questions for the AQA Further Maths (7367), Unit 3: Optional application 1: mechanics, written with Revision Ninja.

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The 20 questions

  1. Which formula gives the x-coordinate of the centre of mass of a uniform lamina under y = f(x)?

    • ∫xy dx / ∫y dx
    • ½∫y² dx / ∫y dx
    • ∫y dx / ∫xy dx
    • ∫x²y dx / ∫y dx

  2. For a uniform lamina, what determines the position of its centre of mass?

    • Its total mass
    • Its material
    • Its shape
    • Its density

  3. Which formula gives the y-coordinate of the centre of mass of a uniform lamina under y = f(x)?

    • ½∫y² dx / ∫y dx
    • ∫xy dx / ∫y dx
    • ∫y² dx / ∫y dx
    • ½∫xy² dx / ∫y dx

  4. For a solid rotated about the x-axis, what gives the x-coordinate of its centre of mass?

    • Integral x y dx / Integral y dx
    • Integral x y^2 dx / Integral y^2 dx
    • Integral x^2 y dx / Integral x dx
    • Integral y^2 dx / Integral x y^2 dx

  5. On which line does the centre of mass of a solid rotated about the x-axis lie?

    • The y-axis
    • The x-axis
    • The line y = -x
    • The line y = x

  6. What is the volume of a solid formed by rotating y = f(x) about the x-axis?

    • Pi integral y^2 dx
    • 2 pi integral y^2 dx
    • Pi integral y dx
    • Integral y^2 dx

  7. For a uniform lamina, its mass is directly proportional to which property?

    • Perimeter
    • Area
    • Thickness
    • Volume

  8. A uniform lamina is the region between y = x and the x-axis for 0 <= x <= 2. What is the x-coordinate of its centre of mass?

    • 2
    • 4/3
    • 1
    • 2/3

  9. For the lamina in the region between y = x and the x-axis for 0 <= x <= 2, what is the y-coordinate of its centre of mass?

    • 1
    • 2/3
    • 1/2
    • 4/3

  10. A uniform lamina is the region between y = 4 - x^2 and the x-axis for 0 <= x <= 2. What is the x-coordinate of its centre of mass?

    • 1
    • 3/4
    • 4/3
    • 2/3

  11. For the lamina in the region between y = 4 - x^2 and the x-axis for 0 <= x <= 2, what is the y-coordinate of its centre of mass?

    • 2
    • 8/5
    • 4/5
    • 16/5

  12. A lamina is the region under y = x^2 for 0 <= x <= 3. What is the x-coordinate of its centre of mass?

    • 2
    • 9/4
    • 81/4
    • 3

  13. The solid formed by rotating y = x for 0 <= x <= 2 about the x-axis is a cone. What is its volume?

    • 8 pi / 3
    • 4 pi
    • 2 pi
    • 16 pi / 3

  14. For the cone formed by rotating y = x for 0 <= x <= 2 about the x-axis, what is the x-coordinate of its centre of mass?

    • 3/2
    • 4/3
    • 2
    • 1

  15. A lamina is the region under y = sqrt(x) for 0 <= x <= 4. What is the x-coordinate of its centre of mass?

    • 12/5
    • 16/5
    • 2
    • 3

  16. The solid formed by rotating the region under y = x^2 for 0 <= x <= 1 about the x-axis has what x-coordinate for its centre of mass?

    • 5/6
    • 2/3
    • 6/5
    • 1/2

  17. A lamina is the region under y = x^2 for 0 <= x <= 1. What is the y-coordinate of its centre of mass?

    • 1/5
    • 1/3
    • 3/10
    • 3/5

  18. A lamina is the region between y = x and y = x^2 for 0 <= x <= 1. What is the x-coordinate of its centre of mass?

    • 1/4
    • 1/2
    • 1/3
    • 2/3

  19. A triangular lamina is bounded by the axes and the line y = 4 - x. What is the x-coordinate of its centre of mass?

    • 4/3
    • 8/3
    • 2
    • 1

  20. A solid is formed by rotating the region under y = sqrt(x) for 0 <= x <= 4 about the x-axis. What is the x-coordinate of its centre of mass?

    • 3/2
    • 4
    • 2
    • 8/3

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