The above ques will be done with the concept of reduced mass...
according to the concept of reduced mass when two bodies rotate about their common centre of mass such that a force of attraction acts between them and the dist.b/n the 2 bodies remains constant then their angular velocites are exactly same both in magnitude and direction .the results for angular velocity and time period that u obtain for single bodies can be obtained by using the reduced mass of 2 body system .To reduce the 2-body system to 1-body just consider 1 body of mass=m(reduced mass) and consider its rotation about a fixed point at a dist=dist between the 2 bodies.thus u get a simple circular motin whose radius is known and the centrifugal force is balanced by the force of attraction that was originally present between the bodies.
we can consider the 2-star system to be as 1 star having a mass
(m1+m2) this will rotate in circular motion about a fixed pt. and having radius equal to the separation b/n the 2 bodies and the force remaining the same towards the centre as b4 which in this case is the gravitation force of interaction.
the equations will be
solving u get w=(1/R)
(G(m1+m2)/R) ie 1/R*root(G(m1+m2)/R)
Hope it helps!