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The length of metallic wire is ℓ1 when tension in it is T1. It is ℓ2 when the tension is T2. The original length of the wire will be -

1. (ℓ1 + ℓ2)/2
2. (T2ℓ1 + T1ℓ2)/(T1 + T2)
3. (T2ℓ1 - T1ℓ2)/(T2 - T1)
4. (T1ℓ1 - T2ℓ2)/(T2 - T1)

Correct answer: (T2ℓ1 - T1ℓ2)/(T2 - T1)

Solution

With l = L0 + k T (k = L0/AY): l1-l2 = k(T1-T2). Solving, L0 = (T1*l2 - T2*l1)/(T1 - T2) = (T2*l1 - T1*l2)/(T2 - T1).

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