Mathematics 9709/42 — October/November 2018

A smooth ring $R$ of mass $m$ kg is threaded on a light inextensible string $ARB$. The ends of the string are attached to fixed points $A$ and $B$ with $A$ vertically above $B$. The string is taut and angle $ARB = 90^{\circ}$. The angle between the part $AR$ of the string and the vertical is $45^{\circ}$. The ring is held in equilibrium in this position by a force of magnitude $2.5$ N, acting on the ring in the direction $BR$ (see diagram). Calculate the tension in the string and the mass of the ring.