Step-by-step explanation:
"Rank the magnitude of the torque the signs exert about the point at which the rod is attached to the side of the building."
Torque is the cross product of the radius vector and force vector.
τ = r × F
The magnitude of the torque is the force times the perpendicular distance. In other words, it is the force times distance times the sine of the angle between them.
τ = F r sin θ
Let's assume the length of each rod is L meters. In each case, the weight is a vertical force, so the perpendicular distance is the horizontal distance between the wall and the sign.
A) τ = (50 kg × 10 m/s²) (L sin 30° m)
τ = 250L Nm
B) τ = (100 kg × 10 m/s²) (L m)
τ = 1000L Nm
C) τ = (50 kg × 10 m/s²) (L sin 60° m)
τ ≈ 433L Nm
D) τ = (90 kg × 10 m/s²) (L m)
τ = 900L Nm
Ranked from greatest to least:
B > D > C > A