A rigid bar of mass 15 kg is supported symmetrically by three wires, each of length 2 m . The wires at the endpoints are made of copper and the middle one is made of steel. If the tension in each wire is the same, then the ratio of the diameter of copper wire to the diameter of steel wire is [Given, Y copper = 1 . 1 × 10 11 N m - 2 and Y steel = 1 . 9 × 10 11 N m - 2 ]

Step-by-step solution

Young's modulus of copper ( Y 1 )   =   1 . 1 × 10 11   N   m - 2 Young's modulus of steel ( Y 2 )   =   1 . 9 × 10 11   N   m - 2 Let d 1 and d 2 be the diameters of copper and steel wires respectively. Since the tension is the same in each wire, therefore each wire has the same extension. Also, as each wire is of the same length, the strain in each of them is the same. Y = F A ∆ l l Y 1 Y 2 = d 2 d 1 2 d 1 d 2 = Y 2 Y 1 = 19 11