A brass wire 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 th

Question

A brass wire 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 1.4T, is ____ °C.

Accepted Answer

Answer: −71 — Stress ∝ ΔT Initial: ΔT₁ = 27 − (−43) = 70 Final: 1.4T ⇒ ΔT₂ = 1.4 × 70 = 98 ⇒ 27 − θ = 98 ⇒ θ = −71°C

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