Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
The diagram depicts a uniform lamina $ABCDEF$ made by taking a semicircle with centre $O$ and radius $1\,\text{m}$ and cutting away a semicircular part with centre $O$ and radius $r\,\text{m}$. The centre of mass of the lamina is on the arc $ABC$. When the lamina is freely suspended at $F$, it hangs in equilibrium.
(i)[4]
Show that the distance, in metres, from $O$ to the centre of mass of the lamina is $\frac{4(1 + r + r^2)}{3\pi(1 + r)}$.
(ii)[3]
Show that $r = 0.494$, accurate to $3$ significant figures.
(iii)[2]
Find the angle that the diameter of the lamina makes with the vertical.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme.