A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity omega. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

Options

A. `(M )/(4m) omega`
B. `( ( M+ 4 m )/( M )) omega`
C. `((M )/( M - 4m )) omega `
D. `((M )/( M + 4m )) omega`

Answer

D

Explanation

According to conservation of angular momentum,
`I omega=` constant
ie, we can write
`I _(1) omega _(1) = I _(2) omega _(2)`
or `MR ^(2) omega = (M + 4m ) R ^(2) omega _(2)`
or `omega _(2) = (( M )/( M + 4 m )) omega`