A steel wire and a copper wire are joined end to end having equal cross-sections. The elongation of two wires is found to be equal under tension. What is the ratio of the length of the steel to the length of copper wire? (Young modulus of steel = 2 . 0 × 10 11 N m - 2 and, Young modulus of copper = 1 . 1 × 10 11 N m - 2 )

Question

A steel wire and a copper wire are joined end to end having equal cross-sections. The elongation of two wires is found to be equal under tension. What is the ratio of the length of the steel to the length of copper wire? (Young modulus of steel = 2 . 0 × 10 11 N m - 2 and, Young modulus of copper = 1 . 1 × 10 11 N m - 2 ), 1 : 2, 2 : 1, 20 : 11, 11 : 20

MARKS App · Accepted Answer

Recall the formula Young's modulus in terms of cross-sectional area and change in length, Y = F A ∆ L L , it means for steel wire and copper wire the change in length is the same, ⇒ ∆ L s t e e l = ∆ L c o p p e r ⇒ T L s t e e l Y s t e e l A = T L c o p p e r Y c o p p e r A ⇒ L s t e e l L c o p p e r = Y s t e e l Y c o p p e r = 2 . 0 × 10 11 1 . 1 × 10 11 = 20 11

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