Under the same load, wire A having length 5.0 m and cross-section 2.5 × 10⁻⁵ m² stretches by the same amount as another wire B of length 6.0 m and cross-section 3.0 × 10⁻⁵ m². The ratio of Young's modulus of wire A to that of wire B is:
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Question

Under the same load, wire A having length 5.0 m and cross-section 2.5 × 10⁻⁵ m² stretches by the same amount as another wire B of length 6.0 m and cross-section 3.0 × 10⁻⁵ m². The ratio of Young's modulus of wire A to that of wire B is:

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G1 Physics · Accepted Answer

Extension ΔL = FL/(AY). Equal extension under same force gives L(A)/[A(A)Y(A)] = L(B)/[A(B)Y(B)]. Thus Y(A)/Y(B) = L(A)A(B)/[L(B)A(A)] = 5×3/(6×2.5)=1.