A uniform beam XY XY\,XY has length 5.6 m and mass 0.6 kg. A sensor of weight λ \lambda\,λ N is fixed at XXX, and a counterweight of weight 4λ 4\lambda\,4λ N is fixed at YYY. The beam is held horizontally in equilibrium by a single vertical cable attached d d\,d m from YYY.
Show that d=5.6λ+1.68g5λ+0.6gd=\dfrac{5.6\lambda+1.68g}{5\lambda+0.6g}d=5λ+0.6g5.6λ+1.68g.