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

The change in length L of a wire is given by the formula L = FL AY , where F is the applied force, L is the original length, A is the cross-sectional area, and Y is Young's modulus of the material. Since both wires are made of the same material, Y is the same for both. The force F applied is also the same. Thus, L L A . The area A is given by r^2 , so L L r^2 . Given the ratio of radii r₁ : r₂ = 2 : 1 and the ratio of lengths L₁ : L₂ = 1 : 2 , we have: L₁ L₂ = ( L₁ L₂ ) ( r₂ r₁ )^2 Substituting the given values: L₁