A wire of length 2 ~m is made from 10 ~cm ³ of copper. A force F is applied so that its length increases by 2 ~mm . Another wire of length 8 ~m is made from the same volume of copper. If the force F is applied to it, its length will increase by

Step-by-step solution

Given, change in length of wire, l₁=2 ~mm , l₂= ?, length of wire, L₁=2 ~m and length of another wire, L₂=8 ~m Change in length, l= F L A Y = F L² (A L) Y = F L² V Y [V=A L] where, Y is Young's modulus. aligned & l L² ( as V, Y and F are constants) & l₂ l₁ = ( L₂ L₁ )²= ( 8 2 )²=16 & l₂=16 l₁=16 2 ~mm &=32 ~mm =3.2 ~cm aligned