From a circular disc of radius R and 9M , a small disc of mass M and radius `(R )/(3)` is removed concentrically .The moment of inertia of the remaining disc about and axis perpendicular to the plane of the disc and passing through its centre is

Options

A. `(40)/(9) MR^(2)`
B. `MR^(2)`
C. `4MR^(2)`
D. `(4)/(9) MR^(2)`

Answer

A

Explanation

`I= (9M (R)^(2))/(2)- (M ((R)/(3))^(2))/(2)`
`= (9MR^(2))/(2)- (MR^(2))/(18)= (80 MR^(2))/(18)`
`= (40MR^(2))/(9)`