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.
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.