If three equal forces F 1 , F 2 and F 3 are acting at the end A of the rod AB, pivoted at the center O, as shown in the diagram given below, then the moment of…

least for F₃ and maximum for F₁

Reason — The moment of a force is the product of the force and the perpendicular distance of its line of action from the pivot. If a force F acts at A at an angle θ with the rod and OA = r, then

$\tau = \text{F r}\sin \theta$

All the three forces are equal and act at the same point A, so the moment of each depends only on the angle θ.

F₃ acts along the rod, so θ = 0° and its line of action passes through O, giving τ₃ = 0, the least.

F₁ acts perpendicular to the rod, so θ = 90° and τ₁ = F r, the maximum.

F₂ acts at an angle between 0° and 90°, so its moment lies between the two.