2. A plank of wood \(X Y\) has length \(5 a\) m and mass 5 kg . It rests on a support at \(Q\), where \(X Q = 3 a\)
m . When a kitten of mass 8 kg sits on the plank at \(P\), where \(P Y = a \mathrm {~m}\), the plank just remains horizontal. By modelling the plank as a non-uniform rod and the kitten as a particle, find

1. the magnitude of the reaction at the support,
2. the distance from \(X\) to the centre of mass of the plank, in terms of \(a\).