5 An object is formed from a uniform circular disc, of radius \(2 a\) and mass \(3 M\), and a uniform \(\operatorname { rod } A B\), of length \(3 a\) and mass \(k M\), where \(k\) is a constant. The centre of the disc is \(O\). The end \(B\) of the rod is rigidly joined to a point on the circumference of the disc so that \(O B A\) is a straight line. The fixed horizontal axis \(l\) is in the plane of the object, passes through \(A\) and is perpendicular to \(A B\).

1. Show that the moment of inertia of the object about the axis \(l\) is \(3 M a ^ { 2 } ( 26 + k )\).
   The object is free to rotate about \(l\).
2. Show that small oscillations of the object about \(l\) are approximately simple harmonic. Given that the period of these oscillations is \(4 \pi \sqrt { } \left( \frac { a } { g } \right)\), find the value of \(k\).