- A thin uniform wire of mass \(12 m\) is bent to form a right-angled triangle \(A B C\). The lengths of the sides \(A B , B C\) and \(A C\) are \(3 a , 4 a\) and \(5 a\) respectively. A particle of mass \(2 m\) is attached to the triangle at \(B\) and a particle of mass \(3 m\) is attached to the triangle at \(C\). The bent wire and the two particles form the system \(S\).
The system \(S\) is freely suspended from \(A\) and hangs in equilibrium.
Find the size of the angle between \(A B\) and the downward vertical.