A thin circular ring of mass M and radius R is rotating about its axis with constant angular velocity `omega`. The objects each of mass m are attached gently to 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

From conservation of angular momentum
`omega_(1)I_(1)=omega_(2)I_(2)`
`:. omega_(2)=(omega_(1)I_(1))/(I_(2))`
or `omega_(2)=omega[(MR^(2))/(MR^(2)+2mR^(2))]=omega((M)/(M+2m))`.