Solving for Tension & Angles in Ball Mass Problem: Help Needed!

[385sk117]

http://ruliweb6.nate.com:8080/ruliboard/gup/img_link7/436/435945_1.jpg

Ball A B
Mass m 2m

Length of tread is 2R where R is the radious of the Circle.
I have to find the tension on the tread and angles
I could have found the angles by assuming that the angle 1 and angle 2 are same
but as balls' masses are different, the angles must be different as well, and if they are different i don't think i can find the angle...
Any helps? Please TT

 

[rl.bhat]

Ball comes rest when
m1*g*sinθ1 = m2*g*sinθ2.
It is given that m2 = 2m1
So sinθ1 = 2*sinθ2...(1)
Length of the thread is 2R and radius is R.
So (θ1 + θ2) = 2R/R = 2 rad.
Put θ2 = (2 - θ1) in the eq.1 and solve for θ1.