A non-uniform girder MN MN\,MN has length 150 cm and mass 18 kg. A worker places a toolkit of mass 12 kg on the girder at LLL, where ML=30ML = 30ML=30 cm. The girder is held in horizontal equilibrium by two vertical supports at M M\,M and N N\,N providing tensions TM T_M\,TM and TNT_NTN.
Given that the tension TN T_N\,TN is 12 N greater than the tension TMT_MTM.
Find the distance, to the nearest cm, of the girder's centre of mass from MMM.
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.