Two wires of diameter 0.25 cm, one made of steel and other made of brass are loaded as shown in figure. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Young's modulus of steel is 2.0 × 10 11 and Young's modulus of Brass 0.91 × 10 11 Pa. The elongations of steel and brass wires are respectively

Step-by-step solution

Given, diameter of wires (2r) = 0.25 cm r = 0.125 cm = 1.25 × 10 -3 m For steel wire, Load (F 1 ) = (4 + 6) kgf = 10 × 9.8 N = 98 N Length of steel wire (l 1 ) = 1.5 m Young's modulus (Y 1 ) = 2.0 × 10 11 Pa Young's modulus (Y) = F 1 × l ⁡ 1 A 1 × Δ l ⁡ 1 Change in length Δ l ⁡ 1 = F 1 × l ⁡ 1 A 1 × Y 1 = F 1 × l ⁡ 1 π r 1 2 × Y 1 = 98 × 1.5 3.14 × 1.25 × 10 - 3 2 × 2.0 × 10 11 ​= 1.5 × 10 -4 m For brass wire, Load (F 2 ) = 6 kgf = 6 × 9.8 N = 58.8 N Length of brass wire (l 2 ) = 1.0 m Young's modulus (Y 2 ) = 0.91