Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3 A . If the length of the first wire is increased by l on applying a force F , how much force is needed to stretch the second wire by the same amount?

Step-by-step solution

According to the question, For wire 1 : Area of cross-section =A₁ , Force applied =F₁ and increase in length = l . From the relation of Young's modulus of elasticity, Y= F l A l Substituting the values for wire 1 in the above relation, we get For wire 2: Area of cross-section =A₂ Force applied =F₂ increase in length = l Volume, V=A l or l= V A Substituting the value of l in Eqs. (i) and (ii), we get Y₁= F₁ V A₁^2 l and Y₂= F₂ V A₂^2 l As it is given that the wires are made up of same material, i.e. Y₁=Y₂ aligned F₁