A round disc of moment of inertia `I_(2)` about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia `I_(1)` rotating with an angular velocity `omega` about the same axis. The final angular velocity of the combination of disc is.............

Options

A. `((I_(1)+I_(2))omega)/(I_(1))`
B. `(I_(2)omega)/(I_(1)+I_(2))`
C. `omega`
D. `(I_(1)omega)/(I_(1)+I_(2))`

Answer

D

Explanation

According to conservation of momentum,
`L=L.`
`therefore I_(1)omega=(I_(1)+I_(2))omega.`
`therefore omega.=(I_(1)omega)/(I_(1)+I_(2))`