A long metallic string of mass m, length $\mathcal{l}$, cross –sectional area A and Young’s modulus Y is suspended from one end A. A small object of mass 2m is attached to its lower end B. Then elongation produced in the string is 

 

• A

  $\frac{5}{2}\frac{\mathrm{mgl}}{\mathrm{AY}}$

• B

  $\frac{4\mathrm{mgl}}{\mathrm{AY}}$

• C

  $\frac{3\mathrm{mgl}}{\mathrm{AY}}$

• D

  $\frac{3\mathrm{mgl}}{2\mathrm{AY}}$