4 A uniform rectangular lamina \(A B C D\) has a mass of 8 kg . The side \(A B\) has length 20 cm , the side \(B C\) has length 10 cm , and \(P\) is the mid-point of \(A B\). A uniform circular lamina, of mass 2 kg and radius 5 cm , is fixed to the rectangular lamina to form a sign. The centre of the circular lamina is 5 cm from each of \(A B\) and \(B C\), as shown in the diagram.
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1. Find the distance of the centre of mass of the sign from \(A D\).
2. Write down the distance of the centre of mass of the sign from \(A B\).
3. The sign is freely suspended from \(P\). Find the angle between \(A D\) and the vertical when the sign is in equilibrium.
4. Explain how you have used the fact that each lamina is uniform in your solution to this question.