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. `5/4 omega `
B. `2/3 omega `
C. `4/5 omega `
D. `3/2 omega `

Answer

C

Explanation

`I_(1)omega_(1)=I_(2) omega_(2)`
`(1)/(2)MR^(2)omega=((1)/(2) MR^(2)+(1)/(2)((M)/(4))R^(2))omega_(2)`
omega_(2)=(4)/(5)omega`