The length of metallic wire is l 1 when tension in it is T 1 . It is l 2 when the tension is T 2 . The original length of the wire will be :

Step-by-step solution

Assuming Hooke's law to be valid T ∝ Δ ℓ T = k Δ ℓ Let, ℓ 0 = natural length (original length) ⇒ T = k ℓ - ℓ 0 so, T 1 = k ℓ 1 - ℓ 0   &   T 2 = k ℓ 2 - ℓ 0 ⇒ T 1 T 2 = ℓ 1 - ℓ 0 ℓ 2 - ℓ 0 ⇒ ℓ 0 = T 2 ℓ 1 - T 1 ℓ 2   T 2 - T 1