Mathematics (AS & A Level) · May / June 2025 · Paper 43 · Question 4

30° a° O A P Q B R 25 kg 20 kg m kg Three blocks P, Q and R, of masses 25 kg, 20 kg and m kg 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 a = (see diagram). Find the value of m and the value of a. [6]

Read automatically from the paper; the printed page above is exact.