Mathematics 9709 · AS & A Level · Probability

Probability — practice question

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

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