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 the same force is applied to another steel wire B of double the length and a diameter 2.4 times that of wire A, the elongation in wire B will be:
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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 the same force is applied to another steel wire B of double the length and a diameter 2.4 times that of wire A, the elongation in wire B will be:

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G1 Physics · Accepted Answer

Elongation Δl = FL/(YA). For the same material and force, Δl ∝ L/A ∝ L/d². Hence Δl(B)/Δl(A) = 2/(2.4)² = 2/5.76. Therefore Δl(B) = 0.2×2/5.76 ≈ 0.069 mm = 6.9×10⁻² mm.