A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity `omega` . Another disc of same dimensions but of mass `(1)/(4)` M is placed gently on the first disc co-axially. The angular velocity of the system is

Options

A. `sqrt2 omega`
B. `4omega//5`
C. `3omega//4`
D. `4omega`

Answer

B

Explanation

`I_(1)omega_(1)+I_(2)omega_(2)=(I_(1)+I_(2))omega therefore omega =((MR^(2)omega)/(2)+I_(1)xx0)/(I_(1)+I_(2))`
`therefore omega =(MR^(2)omega)/(2)xx(8)/(MR^(2)5)=(4 omega)/(5)`.