Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A uniform solid cone has base radius $0.4\text{ m}$ and height $4.4\text{ m}$. A uniform solid cylinder has radius $0.4\text{ m}$ and weight equal to the weight of the cone. The cone and cylinder are joined together so that the cone’s base and one circular end of the cylinder touch, with their circumferences matching exactly. The combined body is in equilibrium with its circular base resting on a plane that is inclined at $20^{\circ}$ to the horizontal (see diagram).
(i)[2]

Calculate the least possible value of the coefficient of friction between the plane and the object.

(ii)[4]

Calculate the greatest possible height of the cylinder.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $\mu = W\sin20/(W\cos20)$

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