Given a uniform disc of mass `M` and radius `R`. A small disc of radius `R//2` is cut from this disc in such a way that the distance between the centres of the two discs is `R//2`. Find the moment of inertia of the remaining disc about a diameter of the original disc perpendicular to the line connecting the centres of the two discs

Options

A. `3MR2//32`
B. `5MR2//16`
C. `1MR2//64`
D. none of these

Answer

C

Explanation

Mass is cut disc `m_(1) =M/4`
Moment of inertia of original disc about axis `1`:

`I=1/4MR^(2)`
Moment of inertia of small disc about axis `1`:
`I'=1/4m_(1)(R/2)^(2)+m_(1)(R/2)^(2)`
`5/16m_(1)R^(2)=5/64MR^(2)`
Required moment of inertia
`I-I'=1/4MR^(2)-5/64 MRS^(2)=11/64MR^(2)`