Heat and Thermal ExpansionHard

Question

A brass wire of length 2 m and radius 1 mm at $27^{\circ}C$ is held taut between two rigid supports. Initially it was cooled to a temperature of $- 43^{\circ}C$ 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 $\_\_\_\_$ $\ ^{\circ}C$

Options

A.-86
B.-71
C.-65
D.-80

Solution

$\ T = \alpha YA(27 - ( - 43)$

$$\begin{array}{r} 1.4\text{ }T = \alpha YA(27 - \theta)\#(i) \end{array}$$

using (ii)/(i)

$${1.4 = \frac{27 - \theta}{70} }{27 - \theta = 98\ \therefore\theta = - 71^{\circ}C}$$

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