Solution:
Let the natural length be \(L\). Using Hooke's law, \[l_A = L(1 + T_A/AY)\] and \[l_B = L(1 + T_B/AY)\]. Eliminating \(AY\) gives \[L = \frac{T_B l_A - T_A l_B}{T_B - T_A}\].
Experimental observations show that for given solid material, the magnitude of strain produced is same whether the stress is tensile or compressive. The ratio of tensile stress to longitudinal strain is defined as Young's modulus and is denoted by \(Y = \sigma/e\). The length of a metal wire is \(l_A\) when the tension in it is \(T_A\) and is \(l_B\) when tension is \(T_B\). The natural length of wire is
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