Lesson 4C.3.3

4C.3.3 Toppling and sliding of 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.3.3, Toppling and sliding of 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. A rigid box on a rough plane is about to tip over. What happens to the vertical line through its centre of mass?

    • it falls outside the base, beyond the edge
    • it falls inside the base, near the centre
    • it passes above its top face
    • it passes through its midpoint on the slope

  2. A body on a rough inclined plane slides when which condition holds?

    • tan theta exceeds the coefficient of friction
    • sin theta exceeds the coefficient of friction
    • cos theta exceeds the coefficient of friction
    • tan theta is less than the coefficient of friction

  3. A uniform block has base half-width b and centre of mass at height h above the base, on a slope of angle theta. Which condition gives toppling?

    • tan theta > h/b
    • tan theta < b/h
    • tan theta > 2b/h
    • tan theta > b/h

  4. When a body is on the point of sliding on a rough plane, the friction force equals

    • mu/R
    • mu R
    • R/mu
    • mg sin theta always

  5. A block is on the verge of toppling about a lower edge. Where does the normal reaction act?

    • at the top of the block
    • at the centre of the base
    • at the centre of mass
    • at the edge about which it would tip

  6. A block on a horizontal plane is pushed horizontally. Which condition ensures it does not topple?

    • the vertical line through its centre of mass passes within its base
    • friction is greater than its weight
    • the push passes through its top face
    • the weight of the block is zero

  7. A block is about to slide up a rough incline under an applied force. In which direction does friction act?

    • zero at limiting equilibrium
    • up the slope
    • down the slope
    • perpendicular to the slope

  8. A block rests on a rough slope at 30 degrees with coefficient of friction 0.5. Does it slide?

    • Yes, since cos 30 degrees exceeds 0.5
    • No, since friction always exceeds the weight component
    • No, since sin 30 degrees is less than 0.5
    • Yes, since tan 30 degrees (about 0.577) exceeds 0.5

  9. A uniform box with a square base of width 0.6 m has its centre of mass 0.8 m above the base. What is the critical value of tan theta for toppling on a slope?

    • 1.33
    • 0.3
    • 0.375
    • 0.75

  10. A block of weight 20 N has base half-width 0.5 m and centre of mass 1 m above the base. It is pushed horizontally with a 10 N force applied at height 1 m. What happens?

    • It slides but never topples
    • It is on the point of toppling, since the moments about the lower edge are equal
    • It topples forwards at once
    • It is stable, since the push is less than the weight

  11. A 5 kg block rests in equilibrium on a rough slope at 20 degrees without sliding (g = 10 m/s^2). What is the friction force?

    • 17.1 N
    • 18.2 N
    • 47.0 N
    • 1.7 N

  12. A block is on the point of sliding on a rough plane with coefficient of friction 0.75. What is the angle of the plane?

    • 36.9 degrees
    • 48.8 degrees
    • 41.4 degrees
    • 53.1 degrees

  13. Under what condition does a uniform block topple before it slides on a rough slope?

    • b is greater than h
    • b/h is less than mu
    • b/h is greater than mu
    • mu is less than 1

  14. A 4 kg block rests on a rough horizontal floor with coefficient 0.3 (g = 10 m/s^2). It is pushed horizontally with 10 N and stays at rest. What is the friction force?

    • 12 N
    • 40 N
    • 0 N
    • 10 N

  15. A 2 kg block is on a rough slope where tan theta = 0.5 and friction is limiting (g = 10 m/s^2). What is the normal reaction?

    • 8 sqrt(5) N, about 17.9 N
    • 4 sqrt(5) N, about 8.9 N
    • 20 N
    • 10 N

  16. A block has base half-width 0.4 m and centre of mass height 1.2 m, and rests on a rough slope with coefficient 0.6. As the slope angle increases, what happens first?

    • Sliding, at tan theta = 0.6
    • Toppling, at tan theta = 0.6
    • Toppling, at tan theta = 1/3
    • Sliding, at tan theta = 1/3

  17. A uniform cube of side a rests on a rough slope with coefficient of friction greater than 1. At what slope angle does it topple?

    • arctan(2), about 63.4 degrees
    • 30 degrees
    • 45 degrees
    • 60 degrees

  18. A uniform block of weight 50 N has base half-width 0.2 m and centre of mass height 0.5 m. It is pushed horizontally at the height of its centre of mass on a rough floor. What push first causes toppling?

    • 50 N
    • 20 N
    • 5 N
    • 10 N

  19. Why can a body topple before it slides on a rough incline when the coefficient of friction is large?

    • The base is wider than the centre of mass height
    • The normal reaction increases as the slope steepens
    • Friction always exceeds the weight component, so sliding never occurs
    • The toppling angle, where tan theta equals b/h, is smaller than the sliding angle when the base is narrow compared with the height

  20. A block has b/h = 0.5 and coefficient of friction 0.8 on a rough slope. At what angle does it first move, and how?

    • 14.0 degrees, by toppling
    • 26.6 degrees, by toppling
    • 45 degrees, by sliding
    • 38.7 degrees, by sliding

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