A uniform carbon-fiber beam XYXYXY, which has a length of 5.6 m and a mass of 0.6 kg, is used as part of a high-precision measurement rig. To calibrate the beam, a sensor of weight λ \lambda\,λ Newtons is fixed at end XXX, and a counterweight of weight 4λ 4\lambda\,4λ Newtons is fixed at end YYY. The beam is suspended in a horizontal position of equilibrium by a single vertical cable attached to the beam at a point d d\,d metres from the end YYY.
Show that
d=5.6λ+1.68g5λ+0.6g d = \frac{5.6\lambda + 1.68g}{5\lambda + 0.6g} d=5λ+0.6g5.6λ+1.68g