Finding the mass constant k for a weighted disc with hole

[Roadtrip]

Why do we take the Center of mass to be on the right side rather than on the left?
A uniform circular disc of radius 4a with a circular hole of radius 2a made in the disc.
The mass of L is m and a particle of mass km is now fixed to L at the point P. The system is now suspended from the point S and hangs freely in equilibrium. The diameter ST makes an angle a with the downward vertical through S, where tana=5/6
Find the value of K

Disc before adding weight km at point P has a mass m of coordinates (10/3,0).
https://s26.postimg.org/qczk9oc3t/image.jpg[URL]https://s26.postimg.org/lsdduqseh/image.jpg

 

[mfb]

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[Roadtrip]

 

[mfb]

The center of mass is on a line that goes from S downwards. If P is lower than Q, then it is to the right of the geometric center of the large disk. It does not have to be - for small values of k the hole is more important and the center of mass would be to the left.