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. For a lamina under the curve y = f(x) between x = a and x = b, which formula gives the x-coordinate of its centre of mass?

    • Integral of x y dx divided by integral of y dx
    • Integral of y dx divided by integral of x y dx
    • Integral of x squared y dx divided by integral of y dx
    • Integral of x dx divided by integral of y dx

  2. For a uniform lamina, the centre of mass depends on which of the following?

    • The material the lamina is made from
    • The mass per unit length of the boundary
    • The shape of the lamina
    • The thickness of the lamina

  3. For the lamina under y = f(x) between a and b, which formula gives the y-coordinate of its centre of mass?

    • (1/2) integral of y^2 dx divided by integral of y dx
    • Integral of y dx divided by integral of x dx
    • Integral of x y^2 dx divided by integral of y^2 dx
    • Integral of x y dx divided by integral of x dx

  4. For a solid formed by rotating a region about the x-axis, which formula gives the x-coordinate of its centre of mass?

    • Integral of x y dx divided by integral of y dx
    • Integral of x y^2 dx divided by integral of y^2 dx
    • Integral of x dx divided by integral of y dx
    • Integral of x y^2 dx divided by integral of y dx

  5. By symmetry, the centre of mass of a solid of revolution formed by rotating a region about the x-axis lies on which line?

    • The y-axis
    • The x-axis
    • The line through the origin at 45 degrees to the x-axis
    • The line y = x

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

    • Pi times integral of y^2 dx from a to b
    • Integral of y^2 dx from a to b
    • Pi times integral of y dx from a to b
    • Integral of y dx from a to b

  7. A uniform lamina has mass proportional to which property of the region it occupies?

    • Its perimeter
    • Its area
    • Its volume
    • The sum of its y-values

  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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