A thin uniform circular disc of mass M and radius R is rotating in a horizonatl plane about an axis passing through its centre and perpendicular to its plane with an angular velocity `omega`. Another disc of same thickness and radius but of mass `(1)/(8)` M is placed gently on the first disc coaxially. The anuglar velocity of the system is now

Options

A. `(9)/(8)omega`
B. `(5)/(9)omega`
C. `(1)/(3)omega`
D. `(2)/(9)omega`

Answer

A

Explanation

`I_(1)=(MR^2)/(2),w_(1)=omega`
` I_(2)=(MR^2)/(2)=(M)/(8)(R^2)/(2)`
`(9MR^2)/(8xx2)`
`I_(1)omega_(1)=I_(2)omega_(2)`
`(MR^2)/(2) omega_(1)=(9)/(8)(MR^2)/(2)omega_2`
`omega_(1)=(9)/(8)omega_2`
`omega_(1)=(9)/(8)omega`.