A thin circular ring M and radius r is rotating about its axis with a constant angular velocity omega. Four objects each of mass m are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be...........

A thin circular ring M and radius r is rotating about its axis with a

1.	A thin circular ring M and radius r is rotating about its axis with a constant angular velocity omega. Four objects each of mass m are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be...........
Answer» `((M-4m)omega)/(M+4m)` `(Momega)/(4m)` `(Momega)/(M+4m)` `((M+4m)omega)/(M)` Solution : `I_(1)` = moment of INERTIA of RING + moment of inertia of arrangement of FOUR object each of mass m `I_(1)=MR^(2)+(4m)r^(2)` According to the conservation of angular momentum `=[("Initial angular"),("momentum"),("of ring")]=[("Total angular"),("momentum of"),("system after"),("arrangment of object")]` `Iomega=I_(1)omega_(1)` `therefore Mr^(2)omega=(Mr^(2)+4mr^(2))omega_(1)` `therefore Momega=(M+4m)omega_(1)` `therefore` New angular velocity `omega_(1)=(Momega)/(M+4m)`