A metal wire has length l1 when tension T1 is applied and length l2 when tension T2 is applied. Find the natural (unstretched) length of the wire.

(l1 + l2)/2
sqrt(l1*l2)
(l1*T2 - l2*T1)/(T2 - T1)
(l1*T2 + l2*T1)/(T2 + T1)

Correct answer: (l1*T2 - l2*T1)/(T2 - T1)

Solution

Let L0 be natural length and k = L0/(AY) (constant). Then l1 = L0 + k*T1 and l2 = L0 + k*T2. Subtracting: l1 - l2 = k(T1 - T2), so k = (l1-l2)/(T1-T2). Substituting back and solving for L0 gives L0 = (l1*T2 - l2*T1)/(T2 - T1).

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