To determine the moment of the force about point $O$, we use the formula for the moment (or torque):

$M = F \times d$

Where:

• $M$ is the moment (in Newton-meters, $N \cdot m$),
• $F$ is the force applied (in Newtons, $N$),
• $d$ is the perpendicular distance from the point $O$ to the line of action of the force (in meters, $m$).

From the image:

• The force $F = 100 \, N$ is applied to the bar.
• The total length from point $O$ to where the force is applied is $5 \, m$ (i.e., $2 \, m + 3 \, m$).

Since the force is applied horizontally, and the distance is perpendicular to the force, we can directly multiply:

$M = 100 \, N \times 5 \, m = 500 \, N \cdot m$

Thus, the correct moment is $500 \, N \cdot m$.

The correct answer seems to be missing from the options given, so the appropriate choice would be "None of the above".

Would you like any additional details or have further questions?

Here are 5 related questions for further exploration:

1. What is the significance of the direction of force in determining the moment?
2. How would the moment change if the force was applied at a different angle?
3. What happens to the moment if the distance is reduced by half?
4. Can a force produce zero moment? If so, under what conditions?
5. How does the moment arm affect the rotational effect of a force?

Tip: The moment increases with the distance from the pivot point (in this case, point $O$).