Question

a metal rod of Young's modulus 2×10^10 under goes elastic strain 0.02% the energy pre unit volume stored in rod in joule/m^

Answer 1

Young's Modulus = Y = stress/strain = σ / ε

Given   Y = 2 * 10¹⁰ Pa
             strain = ε = 0.02 % = 0.0002 = 2 * 10⁻⁴

Energy per unit volume =  U = 1/2 * stress * strain²
    U = 1/2 * σ * ε²
       = 1/2 * Y ε * ε²
       = 1/2 * 2 * 10¹⁰ * (2 * 10⁻⁴)³   J/m³
       = 8 * 10⁻² J/m³
  

Answer 2

Answer:

Young's modulus = stress/strain

given , Y= 2*10^10 Pa

strain = 0.02% = 0.0002= 2*10^-4

energy per unit volume = U= 1/2*stress*strain^2

U=1/2*2*10^10*(2*10^-4)^3 J/m^3

U = 8*10^-2 J/m^3

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