Lesson 4C.3.1

4C.3.1 Centre of mass of uniform and non-uniform rigid bodies Quiz: Pearson Edexcel Further Maths, Unit 32

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4C.3.1, Centre of mass of uniform and non-uniform rigid bodies: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 32: Centres of mass and equilibrium of rigid bodies, written with Revision Ninja.

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The 20 questions

  1. Where is the centre of mass of a uniform rod of length 2a located?

    • At one end
    • Midpoint
    • Outside the rod
    • A distance a/2 from end

  2. A uniform solid hemisphere of radius a has its centre of mass at what distance from the centre of its plane face?

    • a/2
    • 4a/(3 pi)
    • 3a/8
    • 3a/4

  3. A uniform solid cone of height h has its centre of mass at what distance from its base?

    • h/2
    • h/4
    • h/3
    • 3h/8

  4. Where is the centroid of a triangular lamina relative to its base?

    • One third height
    • At the apex
    • Halfway up
    • One quarter height

  5. A uniform semicircular lamina of radius a has its centre of mass at what distance from its straight edge (the diameter)?

    • 4a/(3 pi)
    • 4a/3
    • a/2
    • 3a/(4 pi)

  6. How is the centre of mass of a non-uniform body generally determined?

    • Simple averaging
    • Integration
    • Parallel axis theorem
    • Geometric symmetry

  7. How do you find the centre of mass of a composite rigid body made of known parts?

    • Product of masses
    • Difference of moments
    • Weighted average
    • Sum of coordinates

  8. A uniform rod of mass 2 kg lies from x = 0 to x = 4 m, and a uniform rod of mass 1 kg lies from x = 4 to x = 6 m, forming one straight object. What is the x-coordinate of its centre of mass?

    • 4 m
    • 3.5 m
    • 3 m
    • 2.5 m

  9. A uniform solid hemisphere has radius 6 cm. How far is its centre of mass from the centre of its flat face?

    • 4.5 cm
    • 2.25 cm
    • 3 cm
    • 2.55 cm

  10. A uniform solid cone has perpendicular height 12 cm. How far is its centre of mass from the base?

    • 4 cm
    • 3 cm
    • 6 cm
    • 2 cm

  11. What is the centre of mass distance from the diameter of a uniform semicircular lamina of radius 3 cm?

    • 2/pi cm
    • 3pi/4 cm
    • 4/pi cm
    • 3/pi cm

  12. A rod of length L has density proportional to its distance x from end A. How far from A is its centre of mass?

    • 3L/4
    • L/3
    • 2L/3
    • L/2

  13. A rectangle of size 4 by 2 (area 8, centre (2,1)) is joined to a 2 by 2 square (area 4, centre (5,1)) to form one uniform lamina. What is its centre of mass?

    • (2.5, 1)
    • (3, 1.5)
    • (3.5, 1)
    • (3, 1)

  14. A uniform quarter-circular lamina has radius r. How far is its centre of mass from each straight edge?

    • 2r/3
    • 3r/(4 pi)
    • r/2
    • 4r/(3 pi)

  15. A uniform rod of length 1.2 m and mass 3 kg has a 1 kg particle attached at one end A. How far from A is the centre of mass of the combined body?

    • 0.45 m
    • 0.6 m
    • 0.9 m
    • 0.3 m

  16. A uniform rod of mass 3 kg and length 4 m lies from x = 0 to x = 4 m, with a 2 kg particle attached at x = 4 m. What is the x-coordinate of the centre of mass?

    • 2.8 m
    • 3.2 m
    • 2.4 m
    • 3 m

  17. What is the distance of the centre of mass of a uniform hollow hemispherical shell of radius a from the centre of its plane face?

    • a/2
    • a/3
    • 3a/8
    • 2a/3

  18. A rod lies from x = 0 to x = L with density rho = kx^2. Where is its centre of mass?

    • 3L/4
    • 4L/5
    • L/2
    • 2L/3

  19. A uniform square lamina occupies 0 <= x <= 4 and 0 <= y <= 4. The square 0 <= x <= 2, 0 <= y <= 2 is removed. What is the centre of mass of the remaining lamina?

    • (3/2, 3/2)
    • (2, 2)
    • (8/3, 8/3)
    • (7/3, 7/3)

  20. A uniform L-shaped lamina is made of a 4 by 1 rectangle (0 <= x <= 4, 0 <= y <= 1) and a 1 by 3 rectangle (0 <= x <= 1, 1 <= y <= 4). What is its centre of mass?

    • (9/7, 9/7)
    • (2, 2)
    • (19/14, 19/14)
    • (3/2, 3/2)

All Pearson Edexcel Further Maths quizzes