A small smooth ring $R$, of mass $0.6{\text{ }}kg$, is threaded on a light inextensible string of length $100{\text{ }}cm$.
One end of the string is attached to a fixed point $A$. A small bead $B$ of mass $0.4{\text{ }}kg$ is attached to the other end of the string, and is threaded on a fixed rough horizontal rod which passes through $A$. The system is in equilibrium with $B$ at a distance of $80{\text{ }}cm$ from $A$ (see diagram).
a) Find the tension in the string.
b) Find the frictional and normal components of the contact force acting on $B$.
c) Given that the equilibrium is limiting, find the coefficient of friction between the bead and the rod.

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