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(C) According to Hooke's Law,the tension $T$ in a wire is given by $T = k(l - l_0)$,where $k$ is the force constant and $l_0$ is the unstretched lengt

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$\frac{l_1 T_2 - l_2 T_1}{T_2 - T_1}$

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(C) According to Hooke's Law,the tension $T$ in a wire is given by $T = k(l - l_0)$,where $k$ is the force constant and $l_0$ is the unstretched length.For the first case: $T_1 = k(l_1 - l_0)$ $...(1)$For the second case: $T_2 = k(l_2 - l_0)$ $...(2)$Dividing equation $(1)$ by equation $(2)$:$\frac{T_1}{T_2} = \frac{l_1 - l_0}{l_2 - l_0}$Cross-multiplying gives:$T_1(l_2 - l_0) = T_2(l_1 - l_0)$$T_1 l_2 - T_1 l_0 = T_2 l_1 - T_2 l_0$Rearranging the terms to solve for $l_0$:$T_2 l_0 - T_1 l_0 = T_2 l_1 - T_1 l_2$$l_0(T_2 - T_1) = T_2 l_1 - T_1 l_2$$l_0 = \frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}$

The length of a metal wire is $l_1$ when the tension in it is $T_1$,and it is $l_2$ when the tension is $T_2$. The unstretched length of the wire is

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