Correct vector diagram of forces

[songoku]

Homework Statement

Please see below

Relevant Equations

Equilibrium

The answer is (B) but I don't understand why (C) is wrong. The force acting on the hinge has two components, horizontal and vertical. The horizontal component must be to the right to balance the horizontal component of tension but the vertical component can be either upwards or downwards. Wow to know the correct direction is downwards?

Thanks

 

[robphy]

Hint: What are the conditions for static equilibrium of such an object?

 

[songoku]

Hint: What are the conditions for static equilibrium of such an object?

I get the hint. I need to consider resultant torque at different pivot.

Thank you very much for the help robphy

 

[Lnewqban]

If you replace that hinge with a slider, which is free to move up and down that wall, an external down force would be needed to counteract the moment that W induces about the point of connection of the cable to the trapdoor.