A smooth ring R of mass 0.2kg is threaded on a light 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 ABR = 90°. The angle between the part AR of the string and the vertical is 60°. The ring is held in equilibrium by a force of magnitude XN, acting on the ring in a direction perpendicular to AR (see diagram).

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [M1] For attempt to resolve in one direction. Must use 0.2 substituted for m if just awarding M1 for vertical equation. Must have correct number of relevant terms (forces must have components as required). Allow sin/cos mix. Allow sign errors. Allow g missing.
2. [A1] X sin 60 + T sin 30 - 0.2g = 0. OE. Correct vertical.
3. [A1] X cos 60 - T - T cos 30 = 0. OE. Correct horizontal. If the two Ts are different, they can get max M1A1A0M0A0, unless they subsequently state that the two Ts are equal.
4. [M1] For attempt to solve for tension or X. Must have correct number of relevant terms in both equations. Must get to 'T=' or ‘X='. Allow g missing. Can be implied by correct answers. If no working shown their values must follow from their equations.
5. [A1] X = 2, tension in string = 0.536[N]. Allow exact value of tension = 4-2√3. Allow awrt 2.00 for X.