I've been stuck on this for some time now; to find the tension I would resolve both vertically and horizontally towards the centre of the circle that P travels on - but for this, I require $\sin$/$\cos$ of the angle the rod makes, which in turn requires the radius of P's motion and one other side. I can't deduce this from the text. Is there some other way in which I should be approaching this? I just can't find a way to solve it using alternative methods. Thanks in advance.
Since the radius is perpendicular to the tangent (rod), the angle $\theta$ between the rod and the vertical is given by $$\sin\theta=\frac{r}{2r}=\frac12$$
I hope this helps.