Centre of mass of laminas and composite figuresEdexcel International A Level Further Maths: Mind map

Exam questions on Centre of mass of laminas and composite figures

1. A uniform lamina is made from two rectangles joined together. Rectangle $R_1$ occupies $0\le x\le 6$ and $0\le y\le 2$, and rectangle $R_2$ occupies $0\le x\le 2$ and $2\le y\le 8$, where $x$ and $y$ are distances in cm from the axes.
   Find the distance between the centre of mass of the whole lamina and the centre of mass of $R_1$.2 marks
2. A uniform semicircular lamina of mass $6$ kg has radius $12$ cm and diameter $AB$. The point $O$ is the midpoint of $AB$. Use the result in the formulae booklet for the centre of mass of a semicircular lamina.
   Instead of being attached at $O$, the particle of mass $2$ kg is attached to the lamina at the point on the curved edge on the axis of symmetry. Find the distance of the centre of mass of the combined body from $AB$.2 marks
3. A uniform circular disc has centre $O$ and radius $12$ cm. Circular holes, each of radius $4$ cm, are cut from the disc. Take the $x$-axis through $O$ and the centre $C$ of the first hole, with $OC=6$ cm.
   The first hole is cut out. Find the distance of the centre of mass of the remaining lamina from $O$, and state which side of $O$ it lies.3 marks