How is the total elongation of the bar under its own weight expressed?

Question

A heavy uniform rod of length ‘L’ and material density is hung vertically with its top end rigidly fixed. How is the total elongation of the bar under its own weight expressed?

(a) $\frac{2\delta L^{2}g}{E}$

(b) $\frac{\delta L^{2}g}{E}$

(c) $\frac{\delta L^{2}g}{\sqrt{2E}}$

(d)  $\frac{\delta L^{2}g}{2E}$