In order to determine the Young's Modulus of a wire of radius 0 ....

$Y = \dfrac{Stress}{Strain} = \dfrac{FL}{Al} = \dfrac{mgL}{\pi{R}^{2}l}$

$\dfrac{\DeltaY}{Y} = \dfrac{\Deltam}{m} + \dfrac{\DeltaL}{L} + 2\dfrac{\DeltaR}{R} + \dfrac{\Delta l}{l}$

$\dfrac{\DeltaY}{Y} \times 100 = 100\left[\dfrac{1}{1000} + \dfrac{1}{1000} + 2\left(\dfrac{0 . 001}{0 . 2}\right) + \dfrac{0 . 001}{0 . 5}\right]$

$= \dfrac{1}{10} + \dfrac{1}{10} + 1 + \dfrac{1}{5} = \dfrac{14}{10} = 1 . 4$