Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
$ABCD$ is a uniform lamina in the form of a trapezium with centre of mass $G$. The lines $AD$ and $BC$ are parallel and separated by $1.8\,\text{m}$, with $AD=2.4\,\text{m}$ and $BC=1.2\,\text{m}$ (see diagram).
(i)[4]
Show that $G$ is $0.8\,\text{m}$ from $AD$.
(ii)[2]
Calculate the distance $AG$.
(iii)[5]
The lamina is still freely suspended at $A$ while a horizontal force of magnitude $7$ N acting in the plane of the lamina is applied at $D$. The lamina is in equilibrium with $AG$ making an angle of $10^{\circ}$ with the downward vertical. Find the two possible values for the weight of the lamina.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rectangle: area $= 1.2\times 1.8 = 2.16$, centroid distance $y = 0.9$” …