Heat and Thermodynamics 2 Question 6

9. Steel wire of length L at 40C is suspended from the ceiling and then a mass m is hung from its free end. The wire is cooled down from 40C to 30C to regain its original length L. The coefficient of linear thermal expansion of the steel is 105C, Young’s modulus of steel is 1011N/m2 and radius of the wire is 1mm. Assume that L> diameter of the wire. Then the value of m in kg is nearly.

(2011)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 9. 1.105×1011N/m2,2×105perC

Solution:

  1. Δl1=FLAY=mgLπr2Y= Increase in length

Δl2=LαΔθ= Decrease in length. 

To regain its original length, Δl1=Δl2

mgLπr2Y=LαΔθm=(r2YαΔθg)

Substituting the values we get, m3kg

Answer is 3 .



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