Particles $P$ and $Q$ have masses $0.8{\text{ }}kg$ and $0.4{\text{ }}kg$ respectively. $P$ is attached to a fixed point $A$ by a light inextensible string which is inclined at an angle ${\alpha ^ \circ }$ to the vertical. $Q$ is attached to a fixed point $B$, which is vertically below $A4, by a light inextensible string of length $0.3{\text{ }}m$. The string $BQ$ is horizontal. $P$ and $Q$ are joined to each other by a light inextensible string which is vertical. The particles rotate in horizontal circles of radius $0.3{\text{ }}m$ about the axis through $A$ and $B$ with constant angular speed $5{\text{ }}rad{\text{ }}{s^{ - 1}}$ (see diagram).

a) By considering the motion of $Q$, find the tensions in the strings $PQ$ and $BQ$.

b) Find the tension in the string $AP$ and the value of $\alpha $.