A thin circular ring of mass `m` and radius `R` is rotating about its axis with a constant angular velocity `omega`. Two objects each of mass `M` are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity `omega' =`

Options

A. `(omega M)/(M+m)`
B. `(omega(M-2m))/((M+2m))`
C. `(omegaM)/(M+2m)`
D. `(omega(M+2m))/(M)`

Answer

C

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)`
`therefore omega_(2)=(MR^(2)omega)/((M+2m)R^(2))=(M omega)/(M+2m)`