$A$ thick brass wire of length $L$ and density $\rho$ is suspended from a rigid support. Due to its own weight,$\ell$ is the increase in length. The Young's modulus $Y$ of the brass wire in terms of density is $(g = \text{acceleration due to gravity})$

• A
  $Y = \frac{\rho g L^2}{2 \ell}$
• B
  $Y = \frac{\rho g L^2}{4 \ell}$
• C
  $Y = \frac{\rho g L}{\ell}$
• D
  $Y = \frac{\rho g L^2}{\ell}$