Force diagram of two rods hinged together

[songoku]

Homework Statement

Two identical uniform rods each of weight W are hinged together to form a structure which is resting on rough floor as shown (please see below). If the reaction forces acting on the structure by the floor are $R_1$ and $R_2$, which of the following shows the forces acting on the structure?

Relevant Equations

Resultant torque = 0

Resultant force = 0

Picture from the question

Options:

Option (B) is wrong because the both reaction forces have to be slanted since they are resultant of normal force and frictional force.

I think option (C) is wrong because taking the point where the two rods meet as point P and comparing the torque produced by both weights, the torque by the weight of right rod will be larger since the perpendicular distance is larger so there will be clockwise net torque due to bot weights only. Torque produced by both R₁ and R₂ are also clockwise to the net torque of the system can't be zero.

My guess would be (D) because it seems like R₂ will produce bigger counter clockwise torque to balance the net torque from the weight compared to R₁ in option (A)

Is there a certain way to determine the correct answer?

I also want to ask about the direction of force acting at point P

There will be contact force directed bottom right and friction force directed top right. Is this correct?

Thanks

 

[haruspex]

Is there a certain way to determine the correct answer?

Yes.
It's a hinge, so consider the torque balance about P for each rod separately.

 

[songoku]

Yes.
It's a hinge, so consider the torque balance about P for each rod separately.

Ah I see, so the correct answer is certainly (D)

I just edit my post to show all the attachments in post#1. Is my diagram correct for forces acting on point P?

Thanks

 

[haruspex]

I just edit my post to show all the attachments in post#1. Is my diagram correct for forces acting on point P?

Again, it's a hinge. The reaction force can be in any direction, but it does not involve friction.
To see the direction of that reaction, consider moments about the point where the rod rests on the ground.

 

[songoku]

Thank you very much haruspex