A solid of uniform density is formed from a cylinder and a cone, each with radius $0.5\,\text{m}$ and height $0.4\,\text{m}$. The cone’s circular base is joined to a circular face of the cylinder so that their circumferences line up. The solid is in equilibrium, resting with its circular face on a rough horizontal surface (see diagram). The weight of the solid is $60\,\text{N}$.
(i)[3]
Show that the centre of mass of the solid is $0.275\,\text{m}$ above the surface.
(ii)[2]
Calculate the value of $P$ for which the solid is on the point of toppling.
(iii)[1]
Find the least possible value for the coefficient of friction between the solid and the surface.
(iv)[4]
Show that the solid does not slide, but does topple.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies table of moments for composite lamina” …