As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the smallest?

Answer:
OPTION 5
Explanation:
As the force has no moment arm, it creates no torque about point P.
The option with the smallets torque is about the pivot P is option 5.
The about a given point due to the applied force acting at a perpendicular distance is determined from the product of the applied force and the perpendicular distance.
τ = rFsinθ
where;
For option 5, the angle of the applied force = 0
τ = rFsin(0)
τ = 0
Thus, the option with the smallets torque is about the pivot P is option 5.
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