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

The 20 questions

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

   • at one end
   • one third of its length from one end
   • at its midpoint, a from each end
   • a quarter of its length from one 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?

   • at the apex
   • one third of the height from the base, along the median
   • one half of the height from the base
   • one quarter of the height from the base

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 found?

   • by integration, using the density function over the body
   • by taking the midpoint of its bounding box
   • by dividing its volume by its mass
   • by averaging the positions of its vertices

7. In a composite body made of parts with known centres of mass, how is the overall centre of mass found?

   • treat each part's mass as acting at its own centre of mass and take a weighted average
   • add the centres of mass of the parts
   • use only the largest part
   • average the centres of mass of the parts

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. A uniform semicircular lamina has radius 3 cm. How far is its centre of mass from the diameter?

    • 4/pi cm (about 1.27 cm)
    • 3 cm
    • 1 cm
    • 3/pi cm (about 0.95 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)

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