Finding the angle between AC and horizontal for a rotating lamina

[Kajan thana]

Homework Statement

The lamina is free to rotate about a fixed smooth horizontal axis, perpendicular to the plane of the lamina, passing through the point A. and hangs in equilibrium.
Find the angle between AC and the horizontal.

I have attached a the solution to the question, it seems like there is no line to the question and theta there are showing in the working out.

Homework Equations

I think the answer is 9.46 degree as tanφ= 1/6

The Attempt at a Solution

.[/B]
I have attached screenshot to this thread. Is the solution wrong or have I been thinking in a wrong way? What are looking at that theta shown in the screenshot?

 

[Nidum]

have I been thinking in a wrong way

More like thinking upside down . If you were holding the lamina in the position shown what would happen when you let go of it ?

 

[Kajan thana]

lamina will turn so the centre of mass is below the pivot.

 

[Nidum]

That's it .

 

[Kajan thana]

That's it .

yes but my question why have they goy theata there when they ask for the theta between the horizontal and AC

 

[Kajan thana]

That's it .

i thought about it. It makes sense what they have done.