A uniform disc of mass `m` & radius `R` is pivoted at its centre `O` with its plane vertical as shown in figure `A` circular portion of disc of radius `(R)/(2)` is removed from it. Then choose the correct option(s)

Options

A. Time period of small oscillations of remaining portion about `O` is `pisqrt((13R)/(g))`
B. Time period of small oscillations of remaining portion about `O` is `2pisqrt((13R)/(g))`
C. The centre of mass of the remaining disc is at a distance of `(R)/(6)` from `O`.
D. The centre of mass of the remaining disc is at a distance of `(R)/(8)` from `O`.

Answer

A, C

Explanation

`T = 2pisqrt((I)/(mgy_(cm)))`
`t = (MR^(2))/(2) - ((1)/(2)(M)/(4)((R)/(2))^(2) + (M)/(4)((R)/(2))^(2)) = (13MR^(2))/(32)`
`rArr y_(cm) = (R)/(6)`
`m = (3M)/(4)c`
`T = 2pi , sqrt((1)/(4)(R)/(g))`