Mathematics (AS & A Level) · Oct / Nov 2023 · Paper 41 · Question 5

50Å 40Å B A P 1.6 kg 1.2 kg The diagram shows a particle A, of mass 1.2kg, which lies on a plane inclined at an angle of 40Å to the horizontal and a particle B, of mass 1.6kg, which lies on a plane inclined at an angle of 50Å to the horizontal. The particles are connected by a light inextensible string which passes over a small smooth pulley P fixed at the top of the planes. The parts AP and BP of the string are taut and parallel to lines of greatest slope of the respective planes. The two planes are rough, with the same coefficient of friction, -, between the particles and the planes. Find the value of - for which the system is in limiting equilibrium. [7] 9

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