(i)[3]
Show that it follows that $d = h + \frac{0.04}{h}$.
(ii)[6]
The cone is uniform and has weight $4\,\text{N}$, while the hemispherical shell is uniform and has weight $W\,\text{N}$. Also, $h = 0.8$. Find $W$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
An object is made by joining a hemispherical shell of radius $0.2\,\text{m}$ to a solid cone with base radius $0.2\,\text{m}$ and height $h\,\text{m}$, with the two parts meeting along their circumferences. The centre of mass, $G$, of the object lies $d\,\text{m}$ from the vertex of the cone on the object’s axis of symmetry. The object is in equilibrium on a horizontal plane, with the curved surface of the cone touching the plane (see diagram). The object is about to topple.