A non uniform rod AB AB\,AB has length 200 cm and mass 15 kg. A mass of 10 kg is placed on the rod at CCC, where AC=40AC = 40AC=40 cm. The rod is held in horizontal equilibrium by two light inextensible strings attached at A A\,A and BBB.

Given that the tension in the string at A A\,A is k k\,k N greater than the tension in the string at BBB, find the distance of the rod's centre of mass from A A\,A in terms of kkk.
54 exam-style questions on Edexcel A Level Maths Moments, covering 4.1 Moments, 4.2 Resultant Moments, 4.3 Equilibrium, 4.4 Centres of Mass, and 4.5 Tilting. Each one has a worked solution and a mark scheme showing where the marks go.