Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A uniform solid cone, with height $0.6\,\text{m}$ and mass $0.5\,\text{kg}$, is arranged so that its axis of symmetry is vertical and its vertex $V$ is at the top. The cone has a semi-vertical angle of $60^{\circ}$ and its surface is smooth. It is fixed on a horizontal surface. A particle $P$ of mass $0.2\,\text{kg}$ is attached to $V$ by a light inextensible string of length $0.4\,\text{m}$ (see diagram).
(i)[3]

Calculate the height, above the horizontal surface, of the centre of mass of the cone together with the particle.

(ii)[5]

Show that the tension in the string is $1.96\,\text{N}$, and calculate the magnitude of the force exerted on $P$ by the cone.

(iii)[1]

Calculate the speed of $P$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Takes moments using three terms

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