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 the plane with n angular velocity `omega` another disc of one forth mass and same dimension is gently placed over it coaxially, the angular speed of the composite disc will be ............

Options

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

Answer

C

Explanation

According to law of conservation of momentum,
`I_(1)omega_(1)=I_(2)omega_(2)`
but `I_(1)=(1)/(2)MR^(2)` where M = mass, R = radius) and `I_(2)=(1)/(2)MR^(2)+(1)/(2)((M)/(4)R^(2))`
`=(1)/(2)MR^(2)((5)/(4))=(5MR^(2))/(8)`
and `omega_(1)=omega_(2)`
`therefore (1)/(2)MR^(2)omega=(5)/(8)MR^(2)omega_(2)`
`therefore omega_(2)=(4)/(5)omega`