M3 Vertical circles

Circle with radius r.
Mass is attached to one end of a rod and other end centre of circle.
Rod turns an angle theta from the bottom of the circle.

Resolving to find Tension I can get Tcos(theta)=mg and T=mgcos(theta)

Which is right and why?

I can't quite get what you're asking, but:



Means that if you resolve radially inwards, you get: $T - mg\cos \theta = F_c$ where $F_c$ is the centripetal force.

Do we need to know how to find escape velocity for M3?

Nope.

Why did I revise that then?