How Is Torque Equilibrium Applied to a Sphere Tethered to a Wall?

[accioquote]

Homework Statement

A uniform sphere of weight mg and radius r0 is tethered to a wall by a rope of length ℓ. The rope is tied to the wall a distance h above the contact point of the sphere, as shown in the figure.(Figure 1) The rope makes an angle θ with respect to the wall and is not in line with the ball's center. The coefficient of static friction between the wall and sphere is μ.

To find: a) Frictional force in terms of r0, m, h, theta
b) Suppose the sphere is on the verge of slipping. Derive an expression for coefficient of friction in terms of h and theta.

Homework Equations

Sum(Forces) = 0
Sum(Torques) = 0

The Attempt at a Solution

From Sum(Forces) = 0:
Ff = mg - TCosθ
For torques:
This is where I am confused:
Considering torques with respect to the point of junction between the string and the wall:
In counterclockwise: torque due to tension TLCosθ
In clockwise: torque due to friction?

I'm at a conceptual misunderstanding here!

 

[voko]

Where is Figure 1?

 

[accioquote]

Here it is:

 

[voko]

Because friction is applied at the junction, it cannot have any torque with respect to the junction. But there is another force at a distance from the junction, it is even shown in the figure.

 

[accioquote]

Alright, so that would be the torque due to the force of gravity. What I don't get is how I determine the reference point for calculating the torques. Right now I am using the rope-wall junction.

 

[voko]

It does not matter. Any point will do. Choose one that makes the calculations easiest.