A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane , with a constant angular velocity `omega` Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring . The new angular velocity of the ring will be

Options

A. `4omega`
B. `(M)/(4m)omega`
C. `((M)/(M+4m))omega`
D. `((m)/(M+4m))omega`

Explanation

According to conservation of angular mementurn ,
`Iomega` = constant
ie , we can write
`I_(1)omega_(1)=I_(2)omega_(2)`
or `MR^(2)omega=(M+4m)R^(2)omega_(2)`
or `omega_(2)=((M)/(M+4m))omega`