4. Figure 2
\includegraphics[max width=\textwidth, alt={}, center]{19f831ad-5e32-470c-9974-beb82d5c9753-4_574_1159_395_429} Figure 2 shows a uniform lamina \(A B C D E\) such that \(A B D E\) is a rectangle, \(B C = C D , A B = 8 a\) and \(A E = 6 a\). The point \(X\) is the mid-point of \(B D\) and \(X C = 4 a\). The centre of mass of the lamina is at \(G\).

1. Show that \(G X = \frac { 44 } { 15 } a\).
   (6) The mass of the lamina is \(M\). A particle of mass \(\lambda M\) is attached to the lamina at \(C\). The lamina is suspended from \(B\) and hangs freely under gravity with \(A B\) horizontal.
2. Find the value of \(\lambda\).
   (3)