Three blocks P, Q and R, of masses 25kg, 20kg and mkg respectively, are held in equilibrium by three light inextensible strings OP, OQ and OR. The strings OP and OR both pass over small fixed smooth pulleys A and B respectively, with P and R hanging vertically below the pulleys. The block Q hangs vertically below the point O. The angle between OA and the vertical is 30° and the angle BOQ = α° (see diagram). [Figure 4.1]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [*M1] For resolving in either direction to form an equation – diagram for reference: Correct number of terms. Allow sin/cos mix. Allow sign errors. Allow g missing. Equation must be in terms of m and α only (so no marks until tensions replaced).
2. [A1] 25g cos30-20g - mg cos α = 0 [216.506...-200-10mcosα=0] A0 if g missing.
3. [A1] 25g sin 30 – mg sin α = 0 [125-10msinα = 0] A0 if g missing.
4. [DM1] For attempt to find α. Must get to 'α =' Must come from equations with the correct number of relevant terms.
5. [DM1] For attempt to find m or mg. Must get to 'm='or ‘mg=' OR finding the tension in string OR (for reference if correct is 126.085...) and then using TR = mg. Must come from equations with the correct number of relevant terms.
6. [A1] α=82.5 and m=12.6 AWRT 82.5, 12.6 (α =82.4775... m=12.608...) A0 if g missing from original equations.