The length of a rod under longitudinal tension T₁ is L₁ and that under longitudinal tension T₂ is L₂ . What is the actual length of the rod, in the absence of tensions?

Step-by-step solution

Let, the natural length of wire be L₀ . Using Hooke's law, Y= T L₀ A L ...(i) where, Y is Young's modulus of elasticity, T is temperature, A is area and L is change in length, i.e. L=L-L₀ From Eq. (i), we get L-L₀= T L₀ A Y Case 1 When tension is T₁ and length of wire L=L₁ , L₁-L₀= T₁ L₀ A Y ...(ii) Case 2 When tension is T₂ and length of wire L=L₂L₂-L₀= T₂ L₀ A Y ...(iii) Dividing Eq. (ii) by Eq. (iii), we get aligned & L₁-L₀ L₂-L₀ = T₁ T₂ & L₀= L₁ T₂-L₂ T₁ T₂-T₁ aligned