Binary stars of comparable masses rotate under the influence of each other's gravity at a distance  2[Gω2]1/3. Where ω is the angular velocity of each star about center of mass of the system. If difference between the masses of two stars is 6 units, find the ratio of the masses of bigger to smaller  star

Let say distance between two stars is r.Star 1 revolves around COM in circle of radius r1.Star 2 revolves around COM in circle of radius r2.r1+r2=r  and m1r1=m2r2​⇒r1=m2rm1+m2...............1Mutual gravitational force provides centripetal force.​⇒m1r1ω2=Gm1m2r2⇒ω2=Gm1+m2r3  [From eq. 1]​ Or  r=Gm1+m2ω21/3  Compare with given value of r=2Gω21/3⇒m1+m21/3=2​⇒m1+m2=8and m2−m1=6 (given) ​ which gives m1=1 and m2=7 units ⇒m1m2=17