Steel wire of length 'L' at 40°C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10–5 /°C. Young's modulus of steel is 1011 N/m2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly.

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Physics

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Steel wire of length 'L' at 40°C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^–5 /°C. Young's modulus of steel is 10¹¹ N/m² and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly.

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$ΔL = \frac{mgL}{AY} = Lα (Δθ)$

$\Rightarrow m = \frac{AYα (Δθ)}{g} = \frac{π \times 10^{- 6} \times 10^{11} \times 10^{- 5} \times 10}{10}$

m = 3.14 kg $\Rightarrow$ 3 kg

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