1(back after a loooooooong time ... after my boards(10))
i Think this sum is more of a mathematical junkyard than physics........
so if i read the diagram right
then about the hinge the tourque of both the portions circular and straight should be 0 for equilibrium ...........
now the com of the wire is at a distance 2r/pie from or towards the left from the centre(in the diagram at a distance (r-2r/pie) the wieght can be assumed to act from this point
now taking the mass per unit length to be x....
therefore equationg torques
(x*pie*r)(the masss of circle)g(r-2r/pie)=(x*a)(the mass)*g*a/2
equate it and get the answer
