A thin uniform metallic rod of length $$L$$ and radius $$R$$ rotates with an angular velocity $$\omega$$ in a horizontal plane about a vertical axis passing through one of its ends. The density and the Young's modulus of the material of the rod are $$\rho$$ and $$Y$$ respectively. The elongation in its length is

A

$$\frac{\rho\omega^2L^3}{6Y}$$

B

$$\frac{\rho\omega^2L^3}{3Y}$$

C

$$\frac{\rho\omega^2RL^2}{2Y}$$

D

$$\frac{\rho\omega^2L^3}{2Y}$$