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 M/4 is placed gently on the first disc coaxially. The angular velocity of the system now is

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 its plane with an angular velocity omega. Another disc of same dimensions but of mass M/4 is placed gently on the first disc coaxially. The angular velocity of the system now is
Answer» `(2 omega)/(sqrt2)` `(4 omega)/(5)` `(5 omega)/(4)` `(3 omega)/(4)` SOLUTION :As no torque is applied , therefore angular momentum is conserved . `therefore I_(1) omega_(1) = I_(2) omega_(2)` or `omega_(2) = (I_(1) omega_(1))/(I_(2)) = (((1)/(2) MR^(2)) omega)/ (((1)/(2) MR^(2) + (1)/(2) (M)/(4) R^(2))) = (4omega)/(5)`