Statics of rigid bodies: Edexcel International A Level Further Maths questions

Every Edexcel International A Level Further Maths exam question on M3.5 Statics of rigid bodies, 2019–2025, with its mark scheme and examiner’s report.

All 19 questions on Statics of rigid bodies, as a list

June 2025, Mechanics 3 (M3), Q6 (14 marks): (a) Show, using algebraic integration, that the centre of mass of a uniform solid hemisphere H of radius a is a distance 3 8 a from O, the centre of its plane f
January 2025, Mechanics 3 (M3), Q4 (12 marks): O y x A B Figure 3 Figure 3 shows a shaded uniform lamina OAB which is in the shape of the region enclosed by the x-axis and the curve with equation y a ax x 1
June 2024, Mechanics 3 (M3), Q5 (12 marks): A uniform right solid circular cone C has radius r and height 4r. (a) Show, using algebraic integration, that the distance of the centre of mass of C from its v
January 2024, Mechanics 3 (M3), Q3 (8 marks): y O 2 x Figure 2 The shaded region in Figure 2 is bounded by the x‑axis, the line with equation x = 2 and the curve with equation y x x 1 4 3 . This region is r
January 2024, Mechanics 3 (M3), Q5 (16 marks): (a) Use algebraic integration to show that the centre of mass of a uniform semicircular disc of radius r and centre O is at a distance 4 3 r π from the diameter
June 2023, Mechanics 3 (M3), Q1 (5 marks): In this question you must show all stages in your working. Solutions relying on calculator technology are not acceptable. y x 3 1 O R Figure 1 The finite region
June 2023, Mechanics 3 (M3), Q3 (8 marks): A uniform solid right circular cone C has base radius r, height H and vertex V. A uniform solid S, shown in Figure 3, is formed by removing from C a uniform sol
January 2023, Mechanics 3 (M3), Q1 (8 marks): 1 O R x y Figure 1 The shaded region R is bounded by the x-axis, the line with equation x = 1, the curve with equation y x 1 and the y-axis, as shown in Figure
January 2023, Mechanics 3 (M3), Q3 (10 marks): A D C B 7a 4 4a 4a O D C 7a 4 4a 4a 6a O A B Figure 3 Figure 4 A square ABCD of side 4a is made from thin uniform cardboard. The centre of the square is O. A ci
June 2022, Mechanics 3 (M3), Q5 (10 marks): (a) Use algebraic integration to show that the centre of mass of a uniform solid hemisphere of radius r is at a distance 3 8 r from the centre of its plane face
January 2022, Mechanics 3 (M3), Q1 (7 marks): O R a x y Figure 1 A uniform lamina is in the shape of the region R. Region R is bounded by the curve with equation y = x(x + a) where a is a positive constant,
January 2022, Mechanics 3 (M3), Q4 (8 marks): O ka 2a Figure 3 A thin uniform right hollow cylinder, of radius 2a and height ka, has a base but no top. A thin uniform hemispherical shell, also of radius 2a,
October 2021, Mechanics 3 (M3), Q7 (14 marks): [You may assume that the volume of a cone of height h and base radius r is 1 3 π r2 h .] A uniform solid right circular cone C, with vertex V, has base radius r
June 2021, Mechanics 3 (M3), Q1 (6 marks): 4a 3a Figure 1 A hollow toy is formed by joining a uniform right circular conical shell C, with radius 4a and height 3a, to a uniform hemispherical shell H, wit
June 2021, Mechanics 3 (M3), Q3 (9 marks): The finite region enclosed by the curve with equation y = 3 – x and the lines x = 0 and y = 0 is rotated through 2π radians about the x-axis, to form a uniform
January 2021, Mechanics 3 (M3), Q1 (8 marks): y 1 a R O x Figure 1 The region R, shown shaded in Figure 1, is bounded by the curve with equation y = 1 x , the line with equation x = 1 , the positive x-axis
January 2021, Mechanics 3 (M3), Q4 (9 marks): 8a 6a Figure 3 A uniform right solid cone C has diameter 6a and height 8a, as shown in Figure 3. The solid S is formed by removing a cone of height 4a from the
October 2020, Mechanics 3 (M3), Q4 (10 marks): (a) Use algebraic integration to show that the centre of mass of a uniform solid hemisphere of radius a is a distance 3 8 a from the centre of its plane face. [
January 2020, Mechanics 3 (M3), Q7 (13 marks): NOT to scale O 1 2 C x y R Figure 3 Figure 3 shows part of the curve C with equation y = x2 + 4. The shaded region R is bounded by C, the line with equation x =

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