A brass wire of length 2 m and radius 1 mm at is held taut between two rigid supports. Initially, it was cooled to a temperature of creating a tension T in the wire. [2026]

Question

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 1.4T, is _________ ${}^{\circ}C$ . [2026]

Smart Achievers · Accepted Answer

(3)

$T = α Y A (27 - (- 43)) . ..(i)$

$1.4 T = α Y A (27 - θ) ...(ii)$

$Using (ii)/(i):$

$1.4 = \frac{27 - θ}{70}$

$27 - θ = 98 ∴ θ = - 71 ° C$

Solution

1 - 80

2 - 65

3 - 71

4 - 86

Ans.
(3)

$T = α Y A (27 - (- 43)) . ..(i)$

$1.4 T = α Y A (27 - θ) ...(ii)$

$Using (ii)/(i):$

$1.4 = \frac{27 - θ}{70}$

$27 - θ = 98 ∴ θ = - 71 ° C$

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