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 wheel now rotates with an angular velocity.

Options

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

Answer

C

Explanation

Since the objects ae placed gently, therefore no external torque is acting on the system. Therefore, angualr momentum is constant.

i.e. `I_(1)omega_(1)=I_(2)omega_(2)`
`Mr^(2)xxomega_(1)=(Mr^(2)+2mr^(2))omega_(2)`
`:. omega_(2)=(Momega)/(M+2m)`