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(B) The tension $T$ developed in a wire fixed between two rigid supports due to a change in temperature $\Delta 	heta$ is given by $T = Y A \alpha \D

Vedclass · Accepted Answer

$-71$

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(B) The tension $T$ developed in a wire fixed between two rigid supports due to a change in temperature $\Delta 	heta$ is given by $T = Y A \alpha \Delta 	heta$,where $Y$ is Young's modulus,$A$ is the cross-sectional area,and $\alpha$ is the coefficient of linear expansion. Initially,the temperature change is $\Delta 	heta_1 = 27 - (-43) = 70 ^\circ C$. So,$T = Y A \alpha (70)$ . . . . . . $(1)$ Let the final temperature be $	heta$. The new temperature change is $\Delta 	heta_2 = 27 - 	heta$. The new tension is $1.4 \ T = Y A \alpha (27 - 	heta)$ . . . . . . $(2)$ Dividing equation $(2)$ by $(1)$: $\frac{1.4 \ T}{T} = \frac{Y A \alpha (27 - 	heta)}{Y A \alpha (70)}$ $1.4 = \frac{27 - 	heta}{70}$ $27 - 	heta = 1.4 	imes 70 = 98$ $	heta = 27 - 98 = -71 ^\circ C$.

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