How's equilibrium possible here? Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when the system is in equilibrium position. And feel free to consider any additional information, you think I forgot to mention.
My doubt goes like this......the gravitational force will be more on its left arm than that of right and hence the torque. So what I think is the rod should attain vertical position with the mass $2m$ at the bottom. But that ain't what happens. Tell me where I'm wrong.
 A: Answer corrected, since (as pointed out by @Georg in the comments) I missed this sentence:

The rod is pivoted at the center 

If the arms apparently are equal then you are right! For equal angles $A$ and arms $d$ the torque $\tau=Fd \cos(A)$ caused by the double mass is double as big. The rod will definitely reach a vertical position, $A=90^ \circ$, where both torques are zero, $\tau_1=\tau_2=0$.

But that ain't what happens.

In that case we have not been told everything in this system. Are there more forces? Is the force $F$ not constant but varying with height?
With the stated information only (and assuming gravity acts), the bar must reach a vertical position.

If the arms were not equally long (as I thought), an non-vertical equilibrium can be reached.
The torques $\tau=Fd \cos(A)$ can be equal at some angle (meaning, no rotation) even with different forces $F$ if the distances $d$ to the rotation point are also different, $d_1 \neq d_2$.
A: But that ain't what happens
If your rod is pivoted at the centre, then it must come to an equilibrium only in the vertical position, with mass 'm' at the top and '2m' at the bottom, in the absensce of any additional forces.
If you are sure that is not what happens, then by all probability, the rod is not pivoted at the centre and steeven has explained the case (in the above answer).
Since, you are not confident about any additional info, this is all I can say.
