Answer
We can rank the situations according to the magnitudes of the force on the rod from the cord:
$(1) = (3) \gt (2)$
Work Step by Step
We can consider the torque about a rotation axis at the hinge.
There is a clockwise torque from the weight of the bar. There must also be a counterclockwise torque from the tension in the cord that is equal in magnitude to the clockwise torque.
In situation (2), the cord pulls directly up on the rod so the tension in the cord can be less than the tension in the cord in situations (1) and (3) while still creating the same magnitude of torque.
In situations (1) and (3), the same vertical component of force is required as in situation (2), so there must be a greater tension in the cord in situation (1) and (3). Since the angle is the same in both cases, the tension in the cord is the same in both cases.
We can rank the situations according to the magnitudes of the force on the rod from the cord:
$(1) = (3) \gt (2)$
