Question

A steel wire 2mm in diameter is just stretched between two points at a temperature of 200C. Determine its tension when the temperature falls to 100C. Linear expansion of steel = 1.1x10-5 K-1. Young’s modulus for steel = 2.1 x 1011N/m2

Answer 1

tension in the wire would be 725 N

we know, Young's modulus = stress/strain

⇒Y = F/A(∆L/L)

from linear expansion,

∆L = Lα∆T

so, Y = F/Aα∆T

⇒F = YAα∆T

here A = πd²/4 , where d is diameter of wire.

so, A = 3.14 × (2 × 10^-3)²/4

= 3.14 × 10^-6 m²

given, Y = 2.1 × 10¹¹ N/m² , α = 1.1 × 10^-5/°C or /K

∆T = 200 - 100C = 100C

now F = 2.1 × 10¹¹ N/m² × 3.14 × 10^-6 m² × 1.1 × 10^-5/°C × 100°C

= 2.1 × 3.14 × 1.1 × 10^(11 - 6 - 5 + 2)

= 7.2534 × 10²

= 725.34 N ≈ 725 N

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Answer 2

$\huge\bold\purple{Answer:-}$

we know, Young's modulus = stress/strain

⇒Y = F/A(∆L/L)

from linear expansion,

∆L = Lα∆T

so, Y = F/Aα∆T

⇒F = YAα∆T

here A = πd²/4 , where d is diameter of wire.

so, A = 3.14 × (2 × 10^-3)²/4

= 3.14 × 10^-6 m²

given, Y = 2.1 × 10¹¹ N/m² , α = 1.1 × 10^-5/°C or /K

∆T = 200 - 100C = 100C

now F = 2.1 × 10¹¹ N/m² × 3.14 × 10^-6 m² × 1.1 × 10^-5/°C × 100°C

= 2.1 × 3.14 × 1.1 × 10^(11 - 6 - 5 + 2)

= 7.2534 × 10²

= 725.34 N ≈ 725 N