Lesson ME5-ME6

ME5-ME6 Equilibrium, toppling and sliding of rigid bodies Quiz: AQA Further Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson ME5-ME6, Equilibrium, toppling and sliding of rigid bodies: 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. A uniform rigid block stands on a horizontal surface. For it to topple about an edge, where must the line of action of its weight lie?

    • Inside the base, as far from the edge as possible
    • Outside the base, beyond the edge
    • Through the top face
    • Through the centre of the base

  2. A body rests on a rough horizontal surface and is on the point of sliding. The friction force then equals:

    • mu mg squared
    • mg
    • mu R
    • R divided by mu

  3. A body on a rough plane inclined at alpha to the horizontal is on the point of sliding. Which equation holds?

    • sin(alpha) = mu
    • tan(alpha) = 1 / mu
    • cos(alpha) = mu
    • tan(alpha) = mu

  4. For a rigid body in equilibrium, what is the sum of the moments of the forces about any point?

    • Equal to the total mass
    • Equal to the total weight
    • Zero
    • Equal to the total force

  5. What is a couple?

    • A force and its reaction acting at the same point
    • Two equal forces in the same direction
    • A single force acting through the centre of mass
    • Two equal and opposite forces with different lines of action

  6. The moment of a couple about any point is:

    • Dependent on the point chosen
    • The same for every point
    • Equal to the sum of the forces
    • Zero at the centre of the couple

  7. For a body on a rough incline to remain in equilibrium, which condition on the friction F and normal reaction R must hold?

    • F = 2 mu R
    • F <= R / mu
    • F >= mu R
    • F <= mu R

  8. A body is on a rough plane inclined at 30 degrees, with coefficient of friction mu = 0.6. Will it remain at rest?

    • Yes, since cos(30) is less than mu
    • Yes, since tan(30) is less than mu
    • No, since tan(30) is greater than mu
    • No, since sin(30) is greater than mu

  9. A uniform block has base width 0.4 m and height 0.6 m, with its centre of mass at its geometric centre. On an incline, what is the tangent of the angle at which it topples?

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

  10. A uniform block with base width 0.4 m and height 0.6 m, and coefficient of friction 0.5 with the incline, is tilted up slowly. What happens first?

    • It topples and slides at the same time at tan(alpha) = 2/3
    • It slides at tan(alpha) = 0.5 before toppling
    • It topples at tan(alpha) = 0.5
    • It slides at tan(alpha) = 2/3 before toppling

  11. A uniform rod AB of length 2 m and mass 4 kg is pivoted at A and held horizontal by a vertical string at B. Taking g = 10 m/s^2, what is the tension in the string?

    • 40 N
    • 80 N
    • 20 N
    • 10 N

  12. A horizontal ground has normal reaction 50 N on a block with coefficient of friction 0.4. What is the limiting friction force?

    • 20 N
    • 125 N
    • 12.5 N
    • 0.4 N

  13. What is the friction force needed to keep a 2 kg block at rest on a rough plane inclined at 30 degrees, with g = 10 m/s^2?

    • 10 N
    • 20 N
    • 5 N
    • 17.3 N

  14. A uniform beam of length 4 m and mass 8 kg rests on supports at its ends, A and B. A 12 kg load hangs 1 m from A. Taking g = 10 m/s^2, what is the reaction at A?

    • 130 N
    • 100 N
    • 70 N
    • 120 N

  15. A uniform beam of length 4 m and weight 80 N is supported at its ends with a 40 N load placed 1 m from A. What is the reaction at B?

    • 30 N
    • 50 N
    • 70 N
    • 120 N

  16. A couple consists of two 6 N forces separated by 2.5 m. What is the magnitude of the moment of the couple?

    • 3 N m
    • 30 N m
    • 12 N m
    • 15 N m

  17. A block of mass 3 kg rests on a rough plane with sin(alpha) = 0.6, cos(alpha) = 0.8, and mu = 0.75. Taking g = 10 m/s^2, what is the friction force when the block is on the point of sliding?

    • 24 N
    • 14.4 N
    • 30 N
    • 18 N

  18. Which pair of conditions must hold for a rigid body in equilibrium under coplanar forces?

    • Resultant force zero only
    • Resultant force equal to the weight and moments equal to the force
    • Resultant force zero and sum of moments zero
    • Resultant moment zero only

  19. What is the moment of a force F about a point at perpendicular distance d from its line of action?

    • F / d
    • F d
    • F d squared
    • F + d

  20. A uniform rod of length 2 m is pivoted at one end and its weight of 20 N acts at its midpoint. What is the moment of the weight about the pivot?

    • 40 N m
    • 10 N m
    • 20 N m
    • 2 N m

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