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Question:

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 the radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly?

9

3

2

5

Solution:

We know that
E = F/A(ΔL/L) => ΔL/L = F/AE . (i)
Also ΔL/L ≈ αΔT (ii)
from (i) and (ii)
F/AE = αΔT => mg = (αΔT)AE => m = αΔTAE/g = 10⁻⁵ * 10 * π * (10⁻³)² * 10¹¹ / 10 = π ≈ 3
So correct answer is 3