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

(c ) Since the objects are placed gently, therfore no external torque is acting on
the system. Hence angular
momentum is constant.


`i.e, I_1 omega_1 = I_2 omega_2`
`Mr^2xx omega_1 = (Mr^2 + 2mr^2)omega^2 (:. omega_1 = omega_2)`
`:. omega_2 = (Moemga)/(M+2m)`