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. `(2)/(3) omega`
B. `(4)/(5) omega`
C. `(3)/(4) omega`
D. `(1)/(3) omega`

Answer

B

Explanation

We have, `I_(1)omega_(1)=I_(2)omega_(2)or omega_(2)=(I_(1))/(I_(2))omega_(1)`
`=((1//2MR^(2)))/((1//2MR^(2))+(1//2)(1//4MR^(2)))omega=(4)/(5)omega`.