A scientific sensor unit, SSS, of mass M M\,M kg is suspended from a horizontal overhead crane beam by two light, inelastic steel cables. The cable attached to point P P\,P on the beam has a length of 2.5 m. The cable attached to point Q Q\,Q on the beam has a length of 1.7 m. The sensor unit hangs in equilibrium at a vertical depth of exactly 1.5 m below the level of the beam.
Show that the tension in the shorter cable is exactly 70% greater than the tension in the longer cable.
Given that the tension in the shorter cable is 3.4g Newtons, calculate the value of MMM.