(i)[4]
Calculate the speed of $P$, given that the tension in the string and the contact force between the cone and $P$ are equal in magnitude.
(ii)[4]
Calculate the greatest angular speed at which $P$ can move on the surface of the cone.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle $P$ with mass $0.5\,\text{kg}$ is connected to the vertex $V$ of a fixed solid cone by a light inextensible string. $P$ is on the smooth curved surface of the cone and travels in a horizontal circle of radius $0.1\,\text{m}$, with its centre on the cone’s axis. The cone’s semi-vertical angle is $60^\circ$ (see diagram).
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolution of forces gives $R\cos30^\circ + T\cos60^\circ = 0.5g$” …
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