Rigid bodies in equilibrium: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 10.1 Rigid bodies in equilibrium, 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 33 questions on Rigid bodies in equilibrium, as a list

June 2025, Mechanics Major, Q4 (7 marks): C B 4 m 50° A A uniform rod AB of mass 3 kg and length 4 m rests with one end A on rough horizontal ground. A light inextensible string has one end attached to
June 2025, Mechanics Major, Q6 (5 marks): 55° 25° B 4 kg A m1kg C m2kg One end of a light inextensible string is attached to a particle A of mass m1 kg. The other end of the string is attached to a seco
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, 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, Q4 (8 marks): B 4m 1.5m 25° A A uniform rod AB has mass 3 kg and length 4 m. The end A of the rod is in contact with rough horizontal ground. The rod rests in equilibrium on
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, Mechanics Minor, Q6 (11 marks): Fig. 6.1 shows three forces of magnitude 15 N, 15 N and 30 N acting on a rigid beam AB of length 6 m. One of the forces of magnitude 15 N acts at A, and the oth
June 2024, AS Mechanics A, Q1 (4 marks): Two horizontal forces of magnitudes 7 N and 15 N act at a point O. The 15 N force acts an angle of ° i above the positive x-axis. The 7 N force acts at an angle
June 2024, AS Mechanics A, Q3 (13 marks): The diagram shows a uniform beam AB, of weight 80 N and length 7 m, resting in equilibrium in a vertical plane. The end A is in contact with a rough vertical wa
June 2023, Mechanics Major, Q4 (6 marks): C 3 N 4N D B 6m 5 N 2N A 8m A rigid lamina of negligible mass is in the form of a rhombus ABCD, where AC = 6 m and BD = 8 m. Forces of magnitude 2 N, 4 N, 3 N a
June 2023, Mechanics Minor, Q5 (12 marks): Fig. 5.1 shows a particle P, of mass 5 kg, and a particle Q, of mass 11 kg, which are attached to the ends of a light, inextensible string. The string is taut a
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 2023, AS Mechanics A, Q6 (11 marks): A uniform beam of length 6 m and mass 10 kg rests horizontally on two supports A and B, which are 3.8 m apart. A particle P of mass 4 kg is attached 1.95 m from
June 2022, Mechanics Major, Q1 (5 marks): 7N 4 N i° 40° PN Three forces of magnitudes 4 N, 7 N and P N act at a point in the directions shown in the diagram. The forces are in equilibrium. (a) Draw a cl
June 2022, Mechanics Major, Q12 (13 marks): C D 1 aW 8 a B i A 60° 30° O The diagram shows a uniform square lamina ABCD, of weight W and side-length a. The lamina is in equilibrium in a vertical plane tha
June 2022, Mechanics Minor, Q4 (10 marks): A uniform beam AB of mass 6 kg and length 5 m rests with its end A on smooth horizontal ground and its end B against a smooth vertical wall. The vertical distan
June 2022, AS Mechanics A, Q1 (7 marks): (a) Fig. 1.1 and Fig. 1.2 show rigid rods with forces acting as marked. The diagrams are to scale, and in each figure the side length of a grid square is 1 metr
June 2022, AS Mechanics A, Q2 (7 marks): Three forces, of magnitudes 33 N, 45 N and P N, act at a point in the directions shown in the diagram. The system is in equilibrium. 33N i 45N PN (a) Draw a tri
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, Q8 (12 marks): A capsule consists of a uniform hollow right circular cylinder of radius r and length 2h attached to two uniform hollow hemispheres of radius r. The centres of
November 2021, Mechanics Minor, Q2 (7 marks): The diagram shows a uniform beam AB that rests with its end A on rough horizontal ground and its end B against a smooth vertical wall. The beam makes an angle o
November 2021, AS Mechanics A, Q2 (9 marks): The vertices of a triangular lamina, which is in the x-y plane, are at the origin O and the points A(4, 0) and B(0, 3). Forces, of magnitude T1 N , T2 N and 10
November 2020, Mechanics Major, Q3 (7 marks): The vertices of a triangular lamina, which is in the x–y plane, are at the origin O and the points A ( , ) 2 3 and B - ( 2 1 , ). Forces i 2 + and j 3 i 2 j are
November 2020, Mechanics Major, Q9 (10 marks): A θ 2a 2a B Fig. 9 Fig. 9 shows a uniform rod AB of length 2a and weight 8W which is smoothly hinged at the end A to a point on a fixed horizontal rough bar. A
November 2020, Mechanics Minor, Q5 (13 marks): A uniform rod AB, of mass 3m and length 2a, rests with the end A on a rough horizontal surface. A small object of mass m is attached to the rod at B. The rod is
November 2020, AS Mechanics A, Q3 (9 marks): Fig. 3 shows a light square lamina ABCD, of side length 0.75 m, suspended vertically by wires attached to A and B so that AB is horizontal. A particle P of mass
November 2020, AS Mechanics A, Q4 (9 marks): Fig. 4 shows a uniform beam of length 2a and weight W leaning against a block of weight 2W which is on a rough horizontal plane. The beam is freely hinged to th
June 2019, Mechanics Major, Q1 (5 marks): Three forces represented by the vectors 4 ,i i 2 j and i k 2 j act at the points with coordinates - + - (0, 0), (3, 0) and (0, 4) respectively. (a) Given that t
June 2019, Mechanics Major, Q13 (17 marks): A a i i D E 4a F x B C Fig. 13 A step-ladder has two sides AB and AC, each of length 4a. Side AB has weight W and its centre of mass is at the half-way point; s
June 2019, Mechanics Minor, Q5 (14 marks): Jack and Jemima are pulling a boat along a straight level canal. The resistance to the motion of the boat is modelled as constant and equal to 1200 N. Jack and
June 2019, AS Mechanics A, Q7 (8 marks): C 4a 30° A 4a B Fig. 7 Fig. 7 shows a uniform rod AB of length 4a and mass m. The end A rests against a rough vertical wall. A light inextensible string is atta
June 2018, AS Mechanics A, Q1 (6 marks): Forces of magnitude 4 N, 3 N, 5 N and R N act on a particle in the directions shown in Fig. 1. 4N 5N 60° 3N i RN Fig. 1 The particle is in equilibrium. Find eac
June 2018, AS Mechanics A, Q6 (11 marks): A uniform rod AB has length 2a and weight W. The rod is in equilibrium in a horizontal position. The end A rests on a smooth plane which is inclined at an angle

Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR MEI A-Level Further Maths past papers.

The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.

841 questions