So far all I've got is that the tension in the string is going to be equal to the torque on the bar, which should just be the force on the bar in the perpendicular direction.
So, I can find the perpendicular components of the force due to gravity on the bar and the force due to the hanging mass.
This is where I'm a bit confused. At this point, I would use the formula:
But I'm not exactly sure what to plug in and where.