A thin circular ring of mass M and radius r is rotating about its axis with 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 angular velocity given by

Options

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

Answer

D

Explanation

As no external torque is acting about the axis, angular momentum of system remains conserved .
`I_(1) omega_(1) = I_(2) omega_(2)`
`implies omega_(2) = (I_(1) omega_(1))/(I_(2)) = (Mr^(2) omega)/(( M + 2m) r^(2)) = (M omega)/(( M + 2m))`