A thin circular ring of mass 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

Options

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

Answer

B

Explanation

Since no external torque is applied to the system, the angular momentum of the system, `Iomega=` constant
`therefore I_(1)omega_(1)=I_(2)omega_(2)" …(1)"`
In this case, `I_(1)=Mr^(2), omega_(1)=omega`
`I_(2)=Mr^(2)+4mr^(2)=r^(2)(M+4m)`
`therefore" from (1), "`
`(Mr^(2))omega=[r^(2)(M+4m)]omega_(2)`
`therefore" "omega_(2)=(Momega)/(M+4m)`