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 ............

A thin uniform circular disc of mass M and radius R is rotating in a h

1.	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 ............
Answer» `(5)/(4)OMEGA` `(2)/(3)omega` `(4)/(5)omega` `(3)/(2)omega` SOLUTION :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`