6.04a Centre of mass of systems of particles and bodies Quiz: OCR Further Maths, Unit 3

The 20 questions

1. Where can gravity be assumed to act on a rigid body?

   • Centre of mass
   • Point of contact
   • Base point
   • Geometric centre

2. In linear motion, a rigid body can be modelled as what?

   • A vector
   • A particle
   • A rod
   • A lamina

3. Where is the centre of mass of a uniform rectangular lamina?

   • One-third up height
   • At a vertex
   • Midpoint of base
   • Intersection of diagonals

4. Find the centre of mass of particles of mass 2 kg at (1, 2) and 3 kg at (4, 2).

   • (2.5, 2)
   • (3, 2)
   • (2.2, 2)
   • (2.8, 2)

5. Two equal masses are at (0, 0) and (6, 8). What is their centre of mass?

   • (6, 8)
   • (3, 4)
   • (4, 3)
   • (0, 0)

6. A composite body is made by adding two shapes. How are their moments combined?

   • Divided
   • Subtracted
   • Multiplied
   • Added together

7. A hole is removed from a lamina. How is its moment treated in composite calculations?

   • Multiplied
   • Added
   • Ignored
   • Subtracted

8. What integration formula finds x-bar for a uniform lamina bounded by y = f(x) and y = 0?

   • Integral(x y dx) / Area
   • Integral(y dx) / Area
   • Integral(x^2 dx) / Area
   • Integral(y^2 dx) / Area

9. What is the y-coordinate formula for a uniform lamina bounded by y = f(x) and the x-axis?

   • 0.5 Integral(x y dx) / Area
   • 0.5 Integral(y^2 dx) / Area
   • Integral(x y dx) / Area
   • Integral(y^2 dx) / Area

10. What integration formula gives x-bar for a solid of revolution generated about the x-axis?

    • Integral(x y^2 dx) / Volume
    • Integral(x y dx) / Volume
    • Integral(x^2 y dx) / Volume
    • Integral(y^2 dx) / Volume

11. Where lies the centre of mass of a solid of revolution about the x-axis?

    • On the y-axis
    • Above the x-axis
    • On the x-axis
    • At the origin

12. A body hangs freely from a pivot. Where is its centre of mass relative to the pivot?

    • To the left
    • Directly above pivot
    • Directly below pivot
    • At the pivot

13. What angle does the vertical make with the side of a suspended rectangular lamina?

    • Always 90 degrees
    • Always 0 degrees
    • Always 45 degrees
    • Depends on dimensions

14. Particles of mass 1 kg, 2 kg, 3 kg lie at x = 0, 2, 4. Find x-bar.

    • 3.00
    • 1.33
    • 2.00
    • 2.67

15. What is the centre of mass of a uniform thin hemispherical shell of radius r from its base?

    • 0.667 r
    • 0.375 r
    • 0.5 r
    • 0.25 r

16. What is the centre of mass of a uniform solid hemisphere of radius r from its base?

    • 0.333 r
    • 0.5 r
    • 0.375 r
    • 0.25 r

17. For a uniform solid cone of height h, how far is the centre of mass from the base?

    • 0.2 h
    • 0.25 h
    • 0.5 h
    • 0.333 h

18. For a uniform hollow cone of height h, how far is the centre of mass from the base?

    • 0.25 h
    • 0.333 h
    • 0.125 h
    • 0.5 h

19. A uniform L-shaped lamina has uniform thickness. How can its centre of mass be found?

    • Assume at vertex
    • Rotate about axis
    • Split into rectangles
    • Use single integral

20. When a body is on the point of toppling, where is its centre of mass?

    • Below the base
    • Outside the base entirely
    • At the geometric centre
    • Above lowest contact point

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