Young’s moduli of the material of wires A and B are in the ratio of 1 : 4 , while its area of cross sections are in the ratio of 1 : 3 . If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]

Step-by-step solution

The formula to calculate the elongation of a metallic wire because of the application of a load can be written as Δ L = F L A Y       . . . 1 The ratio of the elongations for both the wires is, then, calculated as follows- ∆ L 1 ∆ L 2 = F L A 1 Y 1 F L A 2 Y 2 =   A 2 Y 2 A 1 Y 1 = 3 1 × 4 1 = 12 1