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Question

A steel wire of length 4.7 m and cross-sectional area 3.0×105m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0×105m2 under a given load. What is the ratio of the Youngs modulus of steel to that of copper ?

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Solution

Young's Modulus for steel, Ys,
Ys=F×LsAs×δl
Young's Modulus for copper, Yc,
Yc=F×LcAc×δl
YsYc=Ls×AcLc×As F and δl are constant
YsYc=4.7×4.0×1053.5×3.0×105
YsYc=1.79:1

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