Two wire of same material having radius in ratio 2: 1 and lengths in ratio 1: 2 . If same force is applied on them, then ratio of their change in length will be

Step-by-step solution

Given, ratio of radius of two wires r₁: r₂=2: 1 r ₁ r ₂ = 2 1 and ratio in their lengths, 1₁: 1₂=1: 2 l₁ 1₂ = 1 2 When same force is applied on them, then ratio r change in their length l ₁ l ₂ = ? We know that, Young's modulus aligned & Y = Fl A l l = Fl AY & l 1 ~A & I ₁ I ₂ = l ₁ ~A ₁ / l ₂ ~A ₂ = l ₁ ~A ₂ l ₂ ~A ₁ & l ₁ I ₂ = l ₁ l ₂ r ₂^2 r ₁^2 = 1 2 ( 1 2 )^2= 1 8 aligned