A thin and 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` . If another disc of same dimension but mass ml4 is placed gently on the first disc co-axially, then the new angular velocity of the system is

Options

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

Answer

C

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)`
`1/2mR^(2)omega=[1/2mR^(2)+1/2(m/4)R^(2)]omega_(2)=1/2mR^(2)(1+1/4)omega_(2)`
`1/2mR^(2)omega=1/2mR^(2)xx5/4omega_(2)rArr=5/4omega_(2)thereforeomega_(2)=4/5omega`