Particles $P$ and $Q$, of masses $0.2{\text{ }}kg$ and $0.5{\text{ }}kg$ respectively, are connected by a light inextensible string. The string passes over a smooth pulley at the edge of a rough horizontal table. $P$ hangs freely and $Q$ is in contact with the table. A force of magnitude $3.2{\text{ }}N$ acts on $Q$, upwards and away from the pulley, at an angle of ${30^ \circ }$ to the horizontal (see diagram).

a) The system is in limiting equilibrium with $P$ about to move upwards. Find the coefficient of friction between $Q$ and the table.

The force of magnitude $3.2{\text{ }}N$ is now removed and $P$ starts to move downwards.

b) Find the acceleration of the particles and the tension in the string.