Centres of mass of particles and laminas: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 6.1 Centres of mass of particles and laminas, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 22 questions on Centres of mass of particles and laminas, as a list

June 2025, Mechanics Major, Q2 (4 marks): y 4 A 7m B 2m 2 x – 4 – 2 0 2 4 – 2 C km The diagram shows a system of three particles of masses 7m, 2m and km situated in the x-y plane at the points A(-2, 3),
June 2025, Mechanics Minor, Q5 (12 marks): The diagram shows a cuboid frame OABCDEFG where O is the origin of the coordinate system in which the points A, C and E have coordinates (50, 0, 0), (0, 30, 0)
June 2025, AS Mechanics A, Q5 (9 marks): Fig 5.1 shows a uniform triangular lamina OAB where O is the origin of the coordinate system in which the points A and B have coordinates (30, 0) and (90, 50) r
June 2025, AS Mechanics A, Q7 (11 marks): The diagram shows a light square lamina OABC where O is the origin of the coordinate system in which the points A, B and C have coordinates (1, 0), (1, 1) and (
June 2024, Mechanics Major, Q3 (5 marks): 0.5m C A O G r m A circular hole with centre C and radius r m, where r 0 5 . , is cut in a uniform circular disc with 1 centre O and radius 0.5 m. The hole touc
June 2024, Mechanics Minor, Q5 (12 marks): A uniform lamina OABC is in the shape of a trapezium where O is the origin of the coordinate system in which the points A, B and C have coordinates (120, 0), (6
June 2024, AS Mechanics A, Q6 (10 marks): A uniform lamina OABC is in the shape of a trapezium where O is the origin of the coordinate system in which the points A, B and C have coordinates (12, 0), ( a
June 2023, Mechanics Minor, Q6 (14 marks): 3 6 In this question you may use the fact that the volume of a sphere of radius r is r . r 3 Fig. 6.1 shows a container in the shape of an open-topped cylinder.
June 2023, AS Mechanics A, Q5 (13 marks): Fig. 5.1 shows the uniform cross-section of a solid S which is formed from a cylinder by boring two cylindrical tunnels the entire way through the cylinder. The
June 2022, Mechanics Minor, Q6 (13 marks): Fig. 6.1 shows a light rod ABC, of length 60 cm, where B is the midpoint of AC. Particles of masses 3.5 kg, 1.4 kg and 2.1 kg are attached to A, B and C respect
June 2022, AS Mechanics A, Q3 (10 marks): Fig. 3.1 shows a thin rectangular frame ABCD, with part of it filled by a triangular lamina ABD. AD 30 cm and AB x cm . Together they form the composite structu
November 2021, Mechanics Major, Q2 (4 marks): The diagram shows a system of three particles of masses 3m, 5m and 2m situated in the x-y plane at the points A (1, 2), B (2, -2) and C (5, 3) respectively. y 4
November 2021, Mechanics Minor, Q5 (16 marks): Fig. 5.1 shows a solid L-shaped ornament, of uniform density. The ornament is 3 cm thick. The x, y and z axes are shown, along with the dimensions of the orname
November 2021, AS Mechanics A, Q7 (10 marks): The vertices of a uniform triangular lamina, which is in the x-y plane, are at the origin and the points (20, 60) and (100, 0). (a) Determine the coordinates of
November 2021, AS Mechanics B, Q3 (8 marks): In this question you must show detailed reasoning. 1 # [In this question you may use the formula: Volume of cone base area # height.] = 3 The region between the
November 2020, Mechanics Major, Q8 (13 marks): [In this question, you may use the fact that the volume of a right circular cone of base radius r and 1 2 height h is r h . ] r 3 (a) By using integration, show
November 2020, Mechanics Minor, Q1 (6 marks): A uniform solid rectangular prism has cross-section with width w cm and height 24 cm. Another uniform solid prism has cross-section in the shape of an isosceles
November 2020, AS Mechanics A, Q6 (10 marks): Fig. 6.1 shows a solid uniform prism OABCDEFG. The Ox, Oy and Oz axes are also shown. The cross-section of the prism is a trapezium. Fig. 6.2 shows the face OAB
June 2019, Mechanics Major, Q4 (6 marks): 5a A B F 4a C a E D Fig. 4 Fig. 4 shows a uniform lamina ABCDE such that ABDE is a rectangle and BCD is an isosceles triangle. AB 5 a , AE 4 a and CD . The poin
June 2019, Mechanics Minor, Q3 (7 marks): Two identical uniform rectangular laminas, P and Q, each having length ka and width a are fixed together, in the same plane, to form a lamina R. With reference
June 2019, AS Mechanics A, Q4 (9 marks): A shovel consists of a blade and handle, as shown in Fig. 4.1 and Fig. 4.2. The dimensions shown in the figures are in metres. The blade is modelled as a unifor
June 2018, AS Mechanics A, Q4 (9 marks): A uniform lamina ABDE is in the shape of an equilateral triangle ABC of side 12 cm from which an equilateral triangle of side 6 cm has been removed from corner

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