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

Question

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, 1.3 × 10 -2 m; 1.5 × 10 -4 m, 1.5 × 10 -4 m; 1.3 × 10 -4 m, 2.0 × 10 -5 m; 1.8 × 10 -3 m, 1.8 × 10 -3 m; 2.1 × 10 -3 m

MARKS App · Accepted Answer

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 × 10 11 Pa Change in length l ⁡ 2 = F 2 × l ⁡ 2 π r 2 2 × Y 2 = 58.8 × 1.0 3.14 × 1.25 × 10 - 3 2 × 0.91 × 10 11 ​ = 1.3 × 10 -4 m

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