Force equilibrium on the shelf

Steps:

• Resolve force F from bar at angle θ to horizontal shelf: horizontal component F sin θ (inward), vertical component F sin θ (upward).
• Horizontal forces balance: wall horizontal component equals F sin θ in magnitude (outward).
• Vertical forces balance: wall vertical component plus F sin θ equals W1 + W2 downward.
• Thus, wall vertical component is W1 + W2 - F sin θ.

Why B is correct:

• Matches Newton's first law for translational equilibrium, with sin θ giving correct components for the given angle to the shelf.

Why the others are wrong:

• A: Incorrectly uses cos θ for vertical component, violating force resolution.
• C: Wrong vertical subtraction of F cos θ instead of F sin θ.
• D: Assumes same as B but listed differently; however, B precisely fits the sin θ components.

Final answer: B