A wire length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in length is l . If another wire of the same material but double the length and radius is stretched with a force 2F, then increase in length is

Step-by-step solution

Let the length of wire = L Radius = r When a force F is applied, then increase in length = l Since, Young’s modulus Y = F π r 2 l L ⇒ Y = F L π r 2 l …(i) For another wire, Length of wire, L’ = 2L Radius of wire, r’ = 2r Applied force, F’ = 2F ∴ Y = F ' L ' π r 2 l ' where, l ’ = elongation in length = 2 F . 2 L π 2 r 2 . c ' = 4 F L 4 π r 2 l ' Y = F L π r 2 l ' ….(ii) From Eqs. (i) and (ii), we have l ’ = l