A wire of cross-section A is stretched horizontally between two clamps located 2 ℓ meters apart. A weight W kg is suspended from the mid point of the wire. If the mid point sags vertically through a d

Question

A wire of cross-section A is stretched horizontally between two clamps located 2 ℓ meters apart. A weight W kg is suspended from the mid point of the wire. If the mid point sags vertically through a distance x ≪ ℓ the strain produced is :-

TestHub · Accepted Answer

Let A P = BP = ( x 2 + ℓ 2 ) 1/2 . Δ ℓ = 2 ( x 2 + ℓ 2 ) 1/2 − 2 ℓ Δ ℓ = 2 ℓ [ ( 1 + ℓ 2 x 2 ​ ) 1/2 − 1 ] St r ain = 2 ℓ Δ ℓ ​ St r ain = 2 ℓ x 2 / ℓ ​ St r ain = 2 ℓ 2 x 2 ​ .

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