Answer
If the point at which the force is applied is moved up the rod, the tension in the cable increases.
Work Step by Step
We can consider the torque with respect to a rotation axis at the hinge.
There is a clockwise torque from the force $F$ and a counterclockwise torque from the tension in the cable. Since the system is in equilibrium, the magnitudes of these two torques are equal.
If the point at which the force is applied is moved up the rod, the force is applied at a greater distance from the rotation axis. Then the magnitude of the clockwise torque increases. Since the magnitude of the counterclockwise torque from the tension in the cable must be equal in magnitude to the torque from the force $F$, the tension in the cable must increase.
If the point at which the force is applied is moved up the rod, the tension in the cable increases.
