A circular disc of mass M and radius R is rotating with angular velocity `omega` . If two small spheres each of mass m are gently attached to two diametrically opposite points on the edge of the disc, then the new angular velocity of the disc will be

Options

A. `((M+4m)/(M))omega`
B. `((M)/(M+4m))omega`
C. `((M+m)/(M))omega`
D. `((M)/(M+2m))omega`

Answer

B

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)`
`therefore" "(1)/(2)MR^(2)omega=((1)/(2)MR^(2)+2mR^(2))omega'`
`therefore Momega=(M+4m)omega'`
`therefore omega'=((M)/(M+4m))omega`