A uniform disc of mass `m` and radius `R` rotates about a fixed vertical axis passing through its centre with angular velocity `omega`. A particle of same mass `m` and having velocity of `2omegaR` towards centre of the disc collides with the disc moving horizontally and sticks to its rim. Then

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)`
`thereforeomega_(2)=(I_(1))/(I_(2))omega_(1)`
`=((1//2mR^(2)))/((1//2mR^(2)+mR^(2))).omega`
`=(omega)/(3)`
`P_(i)=mv_(i)=m(2omegaR)=2momegaR`
`P_(f)=mv_(f)=m((omega)/(3)R)=(1)/(3)momegaR`
impulse `J=|P_(f)-P_(i)|`
`=sqrt(P_(i)^(2)+P_(f)^(2))` (as `theta=90^(@)`)
`=(sqrt(37))/(3)momegaR`