A composite rod consists of two segments joined end to end. Segment 1 has length L, cross-sectional area A and Young's modulus Y. Segment 2 has length 2L, cross-sectional area 2A and Young's modulus Y/2. The rod is pulled by a tensile force F. Neglect the weight of the rod. What is the total elongation?
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Question

A composite rod consists of two segments joined end to end. Segment 1 has length L, cross-sectional area A and Young's modulus Y. Segment 2 has length 2L, cross-sectional area 2A and Young's modulus Y/2. The rod is pulled by a tensile force F. Neglect the weight of the rod. What is the total elongation?

Options

G1 Physics · Accepted Answer

The same tensile force F acts through both segments because they are connected in series. For segment 1, ΔL₁ = [FL] / [AY]. For segment 2, ΔL₂ = [F(2L)] / [(2A)(Y/2)]. The denominator simplifies to (2A)(Y/2) = AY. Therefore, ΔL₂ = [2FL] / [AY]. Hence total elongation is ΔL = ΔL₁ + ΔL₂ = [FL] / [AY] + [2FL] / [AY] = [3FL] / [AY]. Correct option: C.