A solid metal bar of uniform diameter D and length L is hung vertically. If $$\rho$$ is density and E is the Young’s modulus, then the total elongation due to self weight is

A

$$\frac{\rho L g}{2E}$$

B

$$\frac{\rho L^2 g}{2E}$$

C

$$\frac{\rho E g}{2L^2}$$

D

$$\frac{\rho L^2 g}{E}$$