Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
The diagram depicts a container made up of a bowl with weight $14\,\text{N}$ and a handle with weight $8\,\text{N}$. The bowl is a uniform hemispherical shell with centre $O$ and radius $0.3\,\text{m}$. The handle takes the form of a uniform semicircular arc of radius $0.3\,\text{m}$ and is freely hinged to the bowl at $A$ and $B$, where $AB$ is a diameter of the bowl.
(i)[3]
Calculate the distance from $O$ to the centre of mass of the container for the arrangement shown in the diagram, where the handle is perpendicular to the rim of the bowl.
(ii)[5]
Show that, when the handle is on the rim of the bowl, the centre of mass of the container is $0.118\,\text{m}$ from $O$, correct to $3$ significant figures.
(iii)[2]
In the situation where the handle lies on the rim of the bowl, the container is in equilibrium with the curved surface of the bowl resting on a horizontal table. Determine the angle made with the horizontal by the plane containing the rim of the bowl.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the value of $OG$ using $0.3\sin(\pi/2)/(\pi/2)$” …