Equilibrium of a rigid body — AS & A Level Further Mathematics (9231) questions by topic
Composite-lamina and solid-of-revolution problems make up this topic: locating the centre of mass of a triangular lamina with a removed section, balancing a hemisphere-and-cylinder solid on a plane face, and finding a semi-vertical angle for a cone with a hemisphere removed.
Find and show are the only two top command words across 16 questions from 2023 to 2025 papers, worth from 4 to 8 marks, so a correct diagram of forces and centroids typically carries most of the credit. With no examiner-report extracts logged for this topic, submitting each centre-of-mass derivation for instant marking is the main way to confirm a moment equation balances correctly before moving to a harder composite-solid variant.
May–June 2025, Paper 31
An object is formed by removing a solid hemisphere, radius 2r, from a uniform solid cone, radius 3r and semi-vertical angle theta, where tan(theta) = 1/2. The axes of symmetry of…
Answer this question and get it marked →May–June 2025, Paper 32
An object is formed by removing a solid hemisphere, radius 2r, from a uniform solid cone, radius 3r and semi-vertical angle theta, where tan theta = 1/2. The axes of symmetry of…
Answer this question and get it marked →May–June 2025, Paper 33
An object consists of a uniform lamina with a particle attached. The uniform lamina ABCEFD of mass m is formed from a rectangle ABCD and an isosceles triangle CEF, where F is the…
Answer this question and get it marked →May–June 2025, Paper 34
ABCD is a uniform square lamina of side 6a. Points E and F are on DC and AB respectively and are such that DE = FB = h. The quadrilateral BCEF is removed from the square lamina…
Answer this question and get it marked →May–June 2024, Paper 31
A ring of weight W, with radius a and centre O, is at rest on a rough surface that is inclined to the horizontal at an angle alpha where tan(alpha) = 1/2. The plane of the ring is…
Answer this question and get it marked →May–June 2024, Paper 32
A ring of weight W, with radius a and centre O, is at rest on a rough surface that is inclined to the horizontal at an angle alpha where tan(alpha) = 1/2. The plane of the ring is…
Answer this question and get it marked →May–June 2024, Paper 33
A uniform lamina is in the form of a triangle OBC, with OC = 18a, OB = 24a and angle COB = 90 degrees. The point A on OB is such that OA = x (see diagram). The triangle OAC is…
Answer this question and get it marked →October–November 2024, Paper 31
An object is formed by removing a cylinder of radius (2/3)a and height kh (k < 1) from a uniform solid cylinder of radius a and height h. The vertical axes of symmetry of the two…
Answer this question and get it marked →October–November 2024, Paper 32
The end A of a uniform rod AB of length 6a and weight W is in contact with a rough vertical wall. One end of a light inextensible string of length 3a is attached to the midpoint C…
Answer this question and get it marked →October–November 2024, Paper 33
An object is formed by removing a cylinder of radius (2/3)a and height kh (k < 1) from a uniform solid cylinder of radius a and height h. The vertical axes of symmetry of the two…
Answer this question and get it marked →May–June 2023, Paper 31
An object is formed from a solid hemisphere, of radius 2a, and a solid cylinder, of radius a and height d. The hemisphere and the cylinder are made of the same material. The…
Answer this question and get it marked →May–June 2023, Paper 32
An object is formed from a solid hemisphere, of radius 2a, and a solid cylinder, of radius a and height d. The hemisphere and the cylinder are made of the same material. The…
Answer this question and get it marked →May–June 2023, Paper 33
A uniform lamina is in the form of a triangle ABC, with AC = 8a, BC = 6a and angle ACB = 90 degrees. The point D on AC is such that AD = 3a. The point E on CB is such that CE = x…
Answer this question and get it marked →October–November 2023, Paper 31
A uniform square lamina of side 2a and weight W is suspended from a light inextensible string attached to the midpoint E of the side AB. The other end of the string is attached to…
Answer this question and get it marked →October–November 2023, Paper 32
A uniform lamina is in the form of an isosceles triangle ABC in which AC = 2a and angle ABC = 90 degrees. The point D on AB is such that the ratio DB : AB = 1 : k. The point E on…
Answer this question and get it marked →October–November 2023, Paper 33
A uniform square lamina of side 2a and weight W is suspended from a light inextensible string attached to the midpoint E of the side AB. The other end of the string is attached to…
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