A uniform solid cylinder of mass  $$m$$ and radius $$r$$ rolls along an inclined rough plane of inclination $$45^\circ.$$ If it starts to roll from rest from the top of the plane, then the linear acceleration of the cylinder's axis will be: 

A

$$ \frac{1}{\sqrt{2}}\,g $$

B

$$ \frac{1}{3\sqrt{2}}\,g $$

C

$$ \frac{\sqrt{2}}{3}\,g $$

D

$$ \sqrt{2}\,g $$