One end of a light inextensible string of length $1.2{\text{ }}m$ is attached to a fixed point $O$ on a smooth horizontal surface. Particles $P$, $Q$ and $R$ are attached to the string so that $OP = PQ = QR = 0.4{\text{ }}m$. The particles rotate in horizontal circles about $O$ with constant angular speed $\omega {\text{ }}rad{\text{ }}{s^{ - 1}}$ and with $O$, $P$, $Q$ and $R$ in a straight line (see diagram). $R$ has mass $0.2{\text{ }}kg$, and the tensions in the parts of the string attached to $Q$ are $6{\text{ }}N$ and $10{\text{ }}N$.

a) Show that $\omega  = 5$.

b) Calculate the mass of $Q$.

c) Given that the kinetic energy of $P$ is equal to the kinetic energy of $R$, calculate the tension in the part of the string attached to $O$.