Two identical smooth uniform spheres \(A\) and \(B\) each have mass \(m\). The two spheres are moving on a smooth horizontal surface when they collide with speeds \(u\) and \(2 u\) respectively. Immediately before the collision, \(A\) 's direction of motion makes an angle of \(30^{\circ}\) with the line of centres, and \(B\) 's direction of motion is perpendicular to the line of centres (see diagram). After the collision, \(A\) and \(B\) are moving in the same direction. The coefficient of restitution between the spheres is \(e\).
(a) Find the value of \(e\).

(b) Find the loss in the total kinetic energy of the spheres as a result of the collision.