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

Answer

C

Explanation

Apply the law of conservation of angular momentum,
`l_(1)omega_(1)=l_(2)omega_(2)`
`Mr^(2)omega=(M+2m)r^(2)omega'`
Thus, `" "omega'=(omegaM)/(M+2m)`