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Q.

A tungsten wire, 0.5 mm in diameter, is just stretched between two fixed points at a temperature of 40^oC. Determine the tension in the wire when the temperature falls to 20^oC. (coefficient of linear expansion of tungsten = 4.5 × 10^–6/^oC; Young’s modulus of tungsten = 3.45 × 10¹¹Nm^–2)

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a

7.097N

b

5.097N

c

6.097N

d

3.097N

answer is A.

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Detailed Solution

$r = \frac{0.5}{2} = 0.25 mm = 25 x 10^{- 5} m$

$∆_{θ} = 40 - 20 = 20^{o} C; α = 4.5 x 10^{- 6} /^{o} C$
y = 3.45 x 10¹¹ N/m² ; F = YA $α ∆ θ = {Yπr}^{2} α ∆ θ$
= 3.45 x 10¹¹ x 3.14 x 625 x 10^-10 x 4.5 x 10^-6 x 20
F = 6.091N

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A tungsten wire, 0.5 mm in diameter, is just stretched between two fixed points at a temperature of 40oC. Determine the tension in the wire when the temperature falls to 20oC. (coefficient of linear expansion of tungsten = 4.5 × 10–6/oC; Young’s modulus of tungsten = 3.45 × 1011Nm–2)