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9709 P41 - Jun 2013 - Q5
3921

A light inextensible string has a particle A of mass 0.26 kg attached to one end and a particle B of mass 0.54 kg attached to the other end. The particle A is held at rest on a rough plane inclined at angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac{5}{13}\). The string is taut and parallel to a line of greatest slope of the plane. The string passes over a small smooth pulley at the top of the plane. Particle B hangs at rest vertically below the pulley (see diagram). The coefficient of friction between A and the plane is 0.2. Particle A is released and the particles start to move.

  1. Find the magnitude of the acceleration of the particles and the tension in the string.
  2. Particle A reaches the pulley 0.4 s after starting to move. Find the distance moved by each of the particles.
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