Two massive particles of mass M and m (M>M) are seperated by a distance ‘l’ .They rotate with same angular velocity ‘w’ find the linear velocity of particle m.

They are indeed rotating due to gravity. If there was no gravitational attraction they would each fly off away from each other. As you correctly point out, there is no torque and therefore the angular momentum is conserved. Since there is no external forces, the center of mass must be moving at constant velocity and therefore cannot be rotating. The only way this can happen is if the rotation has the center of mass as its axis. Since they are separated a length l, the center of mass would be xcm=lMm+M from the smaller mass m. Now, there is a constant force on m which is F=GmMl2