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A-LevelMathematicsMechanics9709/52 · Oct/Nov 2017 · Q58 Marks

OAB is a uniform lamina in the shape of a quadrant of a circle with centre O and radius 0.8 m which has its centre of mass at G. The lamina is smoothly hinged at A to a fixed point and is free to rotate in a vertical plane. A horizontal force of magnitude 12N acting in the plane of the lamina is applied to the lamina at B. The lamina is in equilibrium with AG horizontal [Figure 5.1].

  1. (i)Calculate the length AG.[3]
  2. (ii)Find the weight of the lamina.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] OG = 2 × 0.8sin(π/4)/(3π/4) (0.48016...m)
  2. [M1] Uses Pythagoras's Theorem OR the cosine formula.
  3. [A1] AG = 0.572(11...) m
  4. [M1] Uses trigonometry to find angle BAG.
  5. [A1] BAG = 8.5965° =8.6(0)°
  6. [M1] Takes moments about A.
  7. [A1FT] 0.572W = 12 × 2 × 0.8sin45 × sin8.6
  8. [A1] W = 3.55 N

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About this question

Topic
Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2017 Paper 5 Variant 2, question 5.

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