This problem requires information from a diagram ("as shown") to determine the exact position of the pivot point X. Without this information, the problem cannot be solved uniquely.
However, I will make a common assumption for such problems: that the beam is in equilibrium, and the pivot X is located such that the moment due to the beam's weight is balanced by the moment due to force F.
Assumptions:
- The beam is uniform, so its weight acts at its center.
- The beam is in rotational equilibrium, meaning the sum of clockwise moments about the pivot equals the sum of anticlockwise moments.
- Both the beam's weight and force F act downwards.
- The pivot X is located between the point where the weight