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An aluminium rod is designed such that it can undergo a maximum elongation of 5 mm before permanent deformation sets in. If the elastic limit and Young's modulus of aluminium are 2.5 10^8 N m ⁻² and 1.0 10¹¹ N m ⁻² respectively, what is the original length of the rod?

Options

  1. A2 m
  2. B2000 m
  3. C0.2 m
  4. D12.5 m

Correct answer

A. 2 m

Step-by-step solution

Given: Maximum elongation, L = 5 10⁻³ m Elastic limit (maximum stress), = 2.5 10^8 N m ⁻² Young's modulus, Y = 1.0 10¹¹ N m ⁻² Using the relation for Young's modulus: Y = Stress Strain = L L Rearranging for original length L : L = Y L Substituting the given values: L = 1.0 10¹¹ 5 10⁻³ 2.5 10^8 L = 5 10^8 2.5 10^8 L = 2 m Answer: 2 m

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