A hole of radius R/2 is cut from a thin circular plate of raduis R as shown in the figure. If the mass of the remaining plate is M, then find moment of inertia of the plate about an axis through O perpendicular to plane


A. `13/25 MR^(2)`
B. `13/24 MR^(2)`
C. `11/24 MR^(2)`
D. `11/25 MR^(2)`

Options

A. `13/25 MR^(2)`
B. `13/24 MR^(2)`
C. `11/24 MR^(2)`
D. `11/25 MR^(2)`

Answer

B

Explanation

Let the mass of disc without hole =m
The mass of cut out hole of radius `R/2` is `m/4`
`:. m-m/4=M` or `m=4/3M`
Moment of inertia of given body about axis passing through O
`=MI` of complete disc -MI of cut out hole .
`=1/2((4M)/3)R^(2)-[1/2(M/3)(R/2)^(2)+M/3(R/2)^(2)]=13/24 MR^(2)`