Equilibrium of a laminaEdexcel International A Level Further Maths: Mind map

Exam questions on Equilibrium of a lamina

1. A uniform rectangular lamina $ABCD$ has $AB=0.6$ m and $BC=0.4$ m, and mass $3$ kg. Take $g=9.8$ m s$^{-2}$. The lamina is freely suspended from a fixed point and hangs in equilibrium in a vertical plane.
   The lamina is suspended from $A$. Find the vertical distance of $G$ below $A$.2 marks
2. A uniform rectangular lamina $PQRS$ has $PQ=40$ cm, $QR=30$ cm and mass $2$ kg. It is free to rotate in a vertical plane about a smooth fixed horizontal axis through $P$, and hangs in equilibrium.
   The particle is removed. Find the angle that $PQ$ makes with the vertical.2 marks
3. A uniform rectangular lamina $ABCD$ has $AB=30$ cm and $BC=50$ cm. It stands in a vertical plane with the edge $AB$ in contact with a rough plane inclined at an angle $\alpha$ to the horizontal. $AB$ lies along a line of greatest slope, with $A$ the lower end.
   The lamina is on the point of toppling. Find the greatest value of $\alpha$.3 marks