A solid uniform metal bar of diameter D mm and length l mm hangs vertically from its upper end. The density of the material is ρ N/mm3 and its modulus of elasticity is E N/mm2. The total extension of the rod due to its own weight would be

• A. \(\frac{{\rho {l^2}}}{{2E}}\)
• B. \(\frac{{\rho l}}{{2E}}\)
• C. \(\frac{{\rho l}}{{4E}}\)
• D. \(\frac{{\rho {l^2}}}{{4E}}\)