Balancing torques, static equalibrium

[Bu2009]

Homework Statement

A uniform rod of mass M sticks out from a vertical wall and points toward teh floor. If the smaller angle it makes with the wall is theta, and its far end is attached to teh ceiling by a string parallel to the wall, find the tension in the supporting string.

Homework Equations

ok I know that this involves balancing torques and the object is in static equalibrium.
this is a MCAt style question so I'm giving multiple choice answers, I know the answer to the question, but I wasn't sure how it was derived.

The Attempt at a Solution

I know that my downward torque based on the rod is (L/2)Mg sin theta. since net torque is 0, the CCW torque must balance the CW torque, but how does this make T = mg/2?

 

[Hootenanny]

Homework Statement

A uniform rod of mass M sticks out from a vertical wall and points toward teh floor. If the smaller angle it makes with the wall is theta, and its far end is attached to teh ceiling by a string parallel to the wall, find the tension in the supporting string.

Homework Equations

ok I know that this involves balancing torques and the object is in static equalibrium.
this is a MCAt style question so I'm giving multiple choice answers, I know the answer to the question, but I wasn't sure how it was derived.

The Attempt at a Solution

I know that my downward torque based on the rod is (L/2)Mg sin theta. since net torque is 0, the CCW torque must balance the CW torque, but how does this make T = mg/2?

Hi BU2009 and welcome to PF,

Your downward torque is correct. Now consider your upward torque, provided by the tension. At what [perpendicular] distance does this tension act from the pivot (wall)?