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The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are ℓ1 and ℓ2 respectively. The actual length of the metal wire is:

1. (T1ℓ2 − T2ℓ1)/(T1 − T2)
2. (T1ℓ1 − T2ℓ2)/(T1 − T2)
3. (ℓ1 + ℓ2)/2
4. √(T1T2ℓ1 + ℓ2)

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

Solution

With l = l0 + kT, l1 = l0 + kT1 and l2 = l0 + kT2. Eliminating k gives the natural length l0 = (T1 l2 - T2 l1)/(T1 - T2).

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