A metal wire has length L1 when under tension T1 and length L2 when under tension T2. What is 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

From T1 = k(L1 - L0) and T2 = k(L2 - L0), dividing gives T1/T2 = (L1-L0)/(L2-L0). Cross-multiplying and solving for L0 yields L0 = (L1*T2 - L2*T1)/(T2 - T1).

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