Mathematics 9709 · AS & A Level · Forces and equilibrium

Forces and equilibrium — practice question

A smooth ring $R$ of mass $m\ \text{kg}$ is attached to a light inextensible string $ARB$. The string’s ends are fixed at points $A$ and $B$, with $A$ directly above $B$. The string is taut, and angle $ARB = 90^{\circ}$. The angle between the segment $AR$ of the string and the vertical is $45^{\circ}$. The ring is kept in equilibrium in this arrangement by a force of magnitude $2.5\,\text{N}$, acting on the ring in the direction $BR$ (see diagram).
(main)[4]

Calculate the tension in the string and the mass of the ring.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: Resolve the forces horizontally: $T\cos45 + T\cos45 = 2.5\cos45$

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