(i)[3]
Find the tension in the string.
(ii)[2]
Find the least angular speed of $P$ for which the motion is possible.
(iii)[3]
Calculate the magnitude of the force exerted on $P$ by the cylinder given that the speed of $P$ is $1.8\,\text{m s}^{-1}$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A smooth hollow cylinder with internal radius $0.3\,\text{m}$ stands fixed with its axis vertical. One end of a light inextensible string of length $0.5\,\text{m}$ is fastened to a point $A$ on the axis. The free end is attached to a particle $P$ of mass $0.2\,\text{kg}$, and $P$ moves in a horizontal circle on the cylinder’s surface (see diagram).
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gives the correct trigonometric values $\cos\theta=0.8$, $\sin\theta=0.6$ (or equivalent)” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI