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

Options

A. `(2 omega)/(sqrt2)`
B. `(4 omega)/(5)`
C. `(5 omega)/(4)`
D. `(3 omega)/(4)`

Answer

B

Explanation

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)`