Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A solid body is made from a uniform hemisphere of radius $0.4\,\text{m}$ joined to a uniform cylinder of radius $0.4\,\text{m}$, with the circumferences of their circular faces matching. The hemisphere and the cylinder each have weight $20\,\text{N}$. The centre of mass of the body is at the centre $O$ of the common circular face.
(i)[2]
Show that the cylinder’s height is $0.3\,\text{m}$.
(ii)[4]
Find the distance of the centre of mass of the new object from $O$.
(iii)[3]
The new object rests with its hemispherical part on a rough horizontal surface. It is kept in equilibrium by a force of magnitude $P\,\text{N}$ acting along its axis of symmetry, which is inclined at $30^\circ$ to the horizontal. Find $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses moments about the common surface: $20 \times 3 \times 0.4/8 = 20 \times h/2$” …