Equilibrium of a rigid body: past paper questions

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• Question 5Oct/Nov 2025, paper 31Structured9 marks

  A uniform lamina $OABCD$ consists of a rectangle $OACD$ and a triangle $ABC$. The length of $OA$ is $ka$, the length of $OD$ is $2a$, the height of triangle $ABC$ is $h$ and angle $CAB$ is ${45}^{\circ }$ (see diagram).

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• Question 4Oct/Nov 2024, paper 31Structured7 marksHas a diagram

  An object is formed by removing a cylinder of radius $\frac{2}{3}a$ and height $kh$ ($k<1$) from a uniform solid cylinder of radius $a$ and height $h$. The vertical axes of symmetry of the two cylinders coincide.

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• Question 3Oct/Nov 2025, paper 32Structured6 marksHas a diagram

  A uniform lamina $OABCD$ is in the form of a rectangle, $OBCD$, joined along the edge $OB$ to a quarter circle $OAB$. The length of $DO$ is $ka$ and the length of $OB$ is $a$. The lamina rests in a vertical plane with its edge $CB$ on a horizontal surface (see diagram).

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• Question 4May/June 2026, paper 33Structured9 marksHas a diagram

  An object consists of a uniform solid cube of side length $d$, and two uniform solid square-based pyramids. The cube and the pyramids are made of the same material.

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• Question 4May/June 2024, paper 31Structured7 marksHas a diagram

  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 $\tan \alpha =\frac{1}{2}$.

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• Question 4May/June 2024, paper 32Structured7 marksHas a diagram

  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 $\tan \alpha =\frac{1}{2}$.

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• Question 3May/June 2023, paper 33Structured7 marksHas a diagram

  A uniform lamina is in the form of a triangle $ABC$, with $AC=8a$, $BC=6a$ and angle $ACB={90}^{\circ }$. The point $D$ on $AC$ is such that $AD=3a$. The point $E$ on $CB$ is such that $CE=x$ (see diagram).

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• Question 4May/June 2025, paper 33Structured4 marksHas a diagram

  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 midpoint of $CD$. The rectangle has sides $AB=2a$ and $AD=a$.

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• Question 5May/June 2024, paper 33Structured7 marksHas a diagram

  A uniform lamina is in the form of a triangle $OBC$, with $OC=18a$, $OB=24a$ and angle $COB={90}^{\circ }$. The point $A$ on $OB$ is such that $OA=x$ (see diagram). The triangle $OAC$ is removed from the lamina.

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