Two particles \(A\) and \(B\), of masses \(m\) and \(km\) respectively, are connected by a light inextensible string of length \(a\). The particles are placed on a rough horizontal circular turntable with the string taut and lying along a radius of the turntable.

Particle \(A\) is at a distance \(a\) from the centre of the turntable, and particle \(B\) is at a distance \(2a\) from the centre. The coefficient of friction between each particle and the turntable is \(\dfrac15\).

When the turntable rotates with angular speed \(\dfrac25\sqrt{\dfrac ga}\), the system is in limiting equilibrium.

(a) Find the tension in the string, in terms of \(m\) and \(g\).

(b) Find \(k\).