Mathematics 9709/43 — October/November 2018

A small smooth ring $R$ of mass $0.2\text{ kg}$ is threaded onto a light inextensible string $ARB$. The two ends of the string are attached to points $A$ and $B$ on a sloping roof inclined at $45^\circ$ to the horizontal. A horizontal force of magnitude $P\text{ N}$, acting in the plane $ARB$, is applied to the ring. The section $BR$ of the string is perpendicular to the roof and the section $AR$ of the string is inclined at $70^\circ$ to the horizontal (see diagram). The system is in equilibrium. Find the tension in the string and the value of $P$.