In order to solve this question we first need to recall the definition of “moment” (torque):
Moment = Force × Distance
Force - the force vector (meaning the vertical component: F × sinα)
Distance - the moment arm, which is the distance between the point where the force is applied and the axis of rotation (pivot).
We shall indicate:
F1 = the force applied by the pole in option 1.
F2 = the force applied by the pole in option 2.
W = the weight of the rectangle
To simplify things, let’s assume the following:
The length of the longer side of the rectangle is 2L
The datum (an arbitrary starting point) is the point of support, where the rectangle is touching the floor.
Now, we can set a pair of equations, based on the formula of moment and Newton’s third law (action and reaction):
(1) F1 × L = W × L => F1 = W
(2) F2 × 2L = W × L => F2 = W/2
As you can see, the first option requires double the force the second option does. Thus, answer choice 1 is correct.
Note that each equation should be positive on one side and negative on the other, since they represent forces acting in an opposite direction. However, in this case we were only interested in the absolute amount of force needed.
Therefore, the correct answer is 1.
1. Twice as strong
2. Half as strong