5 Two particles \(A\) and \(B\) of masses \(m\) and \(k m\) 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 \(2 a\) from the centre of the turntable. The coefficient of friction between each particle and the turntable is \(\frac { 1 } { 5 }\).
When the turntable is made to rotate with angular speed \(\frac { 2 } { 5 } \sqrt { \frac { \mathrm {~g} } { \mathrm { a } } }\), the system is in limiting equilibrium.

1. Find the tension in the string, in terms of \(m\) and \(g\).
2. Find the value of \(k\).