A non-uniform plank XY XY\,XY has length 400 cm and mass 12 kg. A crate of mass 8 kg is placed on the plank at ZZZ, where XZ=100XZ = 100XZ=100 cm. The plank is held in horizontal equilibrium by two light vertical ropes attached at X X\,X and YYY.
Given that the tension in the rope at X X\,X is 15 N greater than the tension in the rope at YYY.
Find the distance, to the nearest cm, of the plank's centre of mass from XXX.
56 exam-style questions on OCR (MEI) A Level Maths 3.6 Rigid Bodies (A-level only), covering 3.6.1 Moment of a force (A-level only), 3.6.2 Equilibrium of a rigid body (A-level only), 3.6.3 Turning effect of forces (A-level only), and 3.6.4 Weight acting through a point (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.