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

Answer

B

Explanation

(b) Apply law is conservation of angular momentum.
`I_1 omega_1 = I_2 omega_2`
In the given case `I_1 = MR^2`
and `I_2 = MR^2 = 2 mR^2`
and `I_2 = MR^2 = 2 mR^2`
also `omega_1 = omega`
Then `omega_2 = (I_1)/(I_2) omega = (M)/(M + 2m) omega`.