4
\includegraphics[max width=\textwidth, alt={}, center]{b5b63135-6d02-4c4a-835a-9834d2852d6b-2_506_561_1765_735} A uniform square lamina \(A B C D\) of side 6 cm has a semicircular piece, with \(A B\) as diameter, removed (see diagram).

1. Find the distance of the centre of mass of the remaining shape from \(C D\). The remaining shape is suspended from a fixed point by a string attached at \(C\) and hangs in equilibrium.
2. Find the angle between \(C D\) and the vertical.
   \includegraphics[max width=\textwidth, alt={}, center]{b5b63135-6d02-4c4a-835a-9834d2852d6b-3_691_1200_262_434} A uniform rod \(A B\), of mass 3 kg and length 4 m , is in limiting equilibrium with \(A\) on rough horizontal ground. The rod is at an angle of \(60 ^ { \circ }\) to the horizontal and is supported by a small smooth peg \(P\), such that the distance \(A P\) is 2.5 m (see diagram). Find
3. the force acting on the rod at \(P\),
4. the coefficient of friction between the ground and the rod.