M1 June 2012 Q2

EdexcelOld spec7 marksMoments

2.

Figure 1: horizontal rod AB of length 3 m on supports at P and Q, with AP = 0.8 m, QB = 0.6 m and G between P and Q
Figure 1

A non-uniform rod \(AB\) has length 3 m and mass 4.5 kg. The rod rests in equilibrium, in a horizontal position, on two smooth supports at \(P\) and at \(Q\), where \(AP = 0.8\) m and \(QB = 0.6\) m, as shown in Figure 1. The centre of mass of the rod is at \(G\). Given that the magnitude of the reaction of the support at \(P\) on the rod is twice the magnitude of the reaction of the support at \(Q\) on the rod, find

(a) the magnitude of the reaction of the support at \(Q\) on the rod, (3)
(b) the distance \(AG\). (4)
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