Two rods are made from materials that have different Young's moduli. The rods are constructed to have the same length and same cross-sectional area. The same force is hung from the end of each rod. The rod with the smaller Young's modulus will stretch more than the rod with the larger Young's modulus. Is this true or false?

Question

Physics

Bryanna Bishop

16 August, 11:56

Two rods are made from materials that have different Young's moduli. The rods are constructed to have the same length and same cross-sectional area. The same force is hung from the end of each rod. The rod with the smaller Young's modulus will stretch more than the rod with the larger Young's modulus. Is this true or false?

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Answers (1)

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Pablo · Answer 1

This is true, the rod with smaller elastic modulus will stretch more than larger elastic modulus.

Explanation:

σ=E*ε

ε=δ/L

σ=E*δ/L

δ = (σ*L) / E

σ=F/A

δ = (F*L) / (A*E)

As Force, Area and Length is same

δ∞1/E

From the expression as E increase δ will be small, so there will be more stretch for smaller elastic modulus.