Centre of mass of particles and composite bodiesAQA A-Level Further Maths: Mind map

Exam questions on Centre of mass of particles and composite bodies

1. A uniform lamina is L-shaped. It is made from a rectangle $8$ cm by $2$ cm and a rectangle $2$ cm by $4$ cm joined along an edge of length $2$ cm. With axes along the two outer edges meeting at the corner $O$, the first rectangle occupies $0\le x\le8$, $0\le y\le2$ and the second occupies $0\le x\le2$, $2\le y\le6$ (lengths in cm).
   The lamina has mass $0.48$ kg. A particle of mass $0.12$ kg is attached at the point $(8,2)$. Find the $x$-coordinate of the centre of mass of the combined body.2 marks
2. Three particles of masses $2$ kg, $3$ kg and $5$ kg are at the points $(1,2)$, $(4,-1)$ and $(-2,3)$ respectively. All coordinates are in metres.
   A fourth particle of mass $10$ kg is added so that the centre of mass of the four particles is at the origin. Find the coordinates of the fourth particle.2 marks
3. A uniform square lamina $ABCD$ has side $20$ cm. A circular hole of radius $4$ cm is cut from it. Take $A$ as the origin, with $AB$ along the $x$-axis and $AD$ along the $y$-axis, so that the centre of the hole is at $(14,10)$ and $C$ is at $(20,20)$ (lengths in cm).
   Find the distance of the centre of mass of the lamina from $AD$.3 marks