A cylindrical wire of length L and diameter D is subjected to a longitudinal stretching force F . If the material of the wire has a Young's modulus Y and a Poisson's ratio , which of the following represents the magnitude of the decrease in its diameter ( D )?

Step-by-step solution

Longitudinal stress is given by F A , where A = D^2 4 . From the definition of Young's modulus ( Y ), the longitudinal strain is: L L = F A Y = 4F D^2 Y Poisson's ratio ( ) is the ratio of lateral strain to longitudinal strain: = D / D L / L Rearranging for the lateral strain: D D = ( L L ) = ( 4F D^2 Y ) Therefore, the magnitude of the decrease in diameter is: D = D 4F D^2 Y = 4F D Y Answer: 4F D Y