From a disc of radius R and mass m, a circular hole of diamter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

Options

A. `15 MR ^(2) //32`
B. `13MR ^(2) //32`
C. `11MR ^(2) //32`
D. `9 MR ^(2) // 32`

Explanation

`I _("Total disc") = ( MR ^(2))/(2)`
`M _("Removed") (M)/(4)` (Mass `prop` area)
`I _("Rrmoved")` (about same Perpendicular axis)
`(M)/(4) ((R //2) ^(2))/(2) + (M )/(4) ((R)/(2)) ^(2) = ( 3 MR ^(2))/( 32)`
`I _("Reaaing disc") = I _("Total") - I _("Removed")`
`= (MR ^(2))/( 2) - ( 3)/(32) MR ^(2) = (13)/(32) MR ^(2).`