1. Figure 1 A thin uniform rod, of total length \(30 a\) and mass \(M\), is bent to form a frame. The frame is in the shape of a triangle \(A B C\), where \(A B = 12 a , B C = 5 a\) and \(C A = 13 a\), as shown in Figure 1.

1. Show that the centre of mass of the frame is \(\frac { 3 } { 2 } a\) from \(A B\). The frame is freely suspended from \(A\). A horizontal force of magnitude \(k M g\), where \(k\) is a constant, is applied to the frame at \(B\). The line of action of the force lies in the vertical plane containing the frame. The frame hangs in equilibrium with \(A B\) vertical.
2. Find the value of \(k\).