A disc of mass `m` and radius `R` has a concentric hole of radius `r`. Its moment of inertia about an axis through its center and perpendicular to its plane is

Options

A. `(1)/(2)m(R-r)^(2)`
B. `(1)/(2)m(R^(2)-r^(2))`
C. `(1)/(2)m(R+r)^(2)`
D. `(1)/(2)m(R^(2)+r^(2))`

Explanation

`I_(0)=(1)/(2)m_(1) R^(2)-(1)/(2)m_(2)r^(2)`
`m_(1)-m_(2)=m` (`i`)
`m_(1) prop R^(2), m_(2) prop r^(2), (m_(1))/(m_(2))=(R^(2))/(r^(2))` (`ii`)
`m_(1)(1-(r^(2))/(R^(2)))=m=m_(1)=(mR^(2))/(R^(2)-r^(2)),m_(2)=(mr^(2))/(R^(2)-r^(2))`
`I_(0)=(m)/(2(R^(2)-r^(2)))(R^(4)-r^(4))=(1)/(2)m(R^(2)+r^(2))`