4 A uniform rectangular lamina \(A B C D\) has a mass of 5 kg . The side \(A B\) has length 60 cm and the side \(B C\) has length 30 cm . The points \(P , Q , R\) and \(S\) are the mid-points of the sides, as shown in the diagram below. A uniform triangular lamina \(S R D\), of mass 4 kg , is fixed to the rectangular lamina to form a shop sign. The centre of mass of the triangular lamina \(S R D\) is 10 cm from the side \(A D\) and 5 cm from the side \(D C\).
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1. Find the distance of the centre of mass of the shop sign from \(A D\).
2. Find the distance of the centre of mass of the shop sign from \(A B\).
3. The shop sign is freely suspended from \(P\). Find the angle between \(A B\) and the horizontal when the shop sign is in equilibrium.
4. To ensure that the side \(A B\) is horizontal when the shop sign is freely suspended from point \(P\), a particle of mass \(m \mathrm {~kg}\) is attached to the shop sign at point \(B\). Calculate \(m\).
5. Explain how you have used the fact that the rectangular lamina \(A B C D\) is uniform in your solution to this question.
   (1 mark)
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