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 and ratio in their lengths, l₁ l₂ = 1 2 When same force is applied on them, then ratio change in their lengths, l₁ l₂ = ? We known that, Young's modulus, gathered Y= F l A l l= F l A Y l l A l₁ l₂ = l₁ / A₁ l₂ / A₂ = l₁ A₂ l₂ A₂ l₁ l₂ = l₁ / A₁ r₂^2 / r₁^2 = 1 2 ( 1 2 )^2= 1 8 gathered