A brass wire of length 2 m and radius 1 mm at 27^ C is held taut between two rigid supports. Initially it was cooled to a temperature of -43^ C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to

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A brass wire of length 2 m and radius 1 mm at 27^ C is held taut between two rigid supports. Initially it was cooled to a temperature of -43^ C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4 T , is _ _ _ _ ^ C .

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Correct answer: C. -71

Thermal stress in the wire is caused by contraction. At -43°C, the temperature drop from 27°C is T₁ = 70°C It creates tension T = YA T₁ where Y is Young's modulus and is linear expansion coefficient. For tension to increase to 1.4T , the new temperature drop must be: T₂ = 1.4 70 = 98°C . Required temperature: T₃ = 27 - 98 = -71°C

A brass wire of length 2 m and radius 1 mm at 27^ C is held taut between two rigid supports. Initially it was cooled to a temperature of -43^ C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4 T , is _ _ _ _ ^ C .

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