A force is applied to a steel wire A , rigidly clamped at one end. As a result elongation in the wire is 0 . 2 mm . If same force is applied to another steel wire B of double the length and a diameter 2 . 4 times that of the wire A , the elongation in the wire B will be (wires having uniform circular cross sections)

Question

A force is applied to a steel wire A , rigidly clamped at one end. As a result elongation in the wire is 0 . 2 mm . If same force is applied to another steel wire B of double the length and a diameter 2 . 4 times that of the wire A , the elongation in the wire B will be (wires having uniform circular cross sections), 6 . 06 × 10 – 2 mm, 2 . 77 × 10 – 2 mm, 3 . 0 × 10 – 2 mm, 6 . 9 × 10 – 2 mm

MARKS App · Accepted Answer

As we know, Y = F A ∆ l l ⇒ F = Y A l ∆ l For both cases force applied is the same, therefore Y A ∆ l l 1 = Y A ∆ l l 2 ⇒ ∆ l 2 ∆ l 1 = A 1 A 2 × l 2 l 1 ⇒ ∆ l 2 0 . 2 = π R 2 π 2 . 4 R 2 × 2 1 ⇒ ∆ l 2 = 6 . 9 × 10 - 2 mm

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