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. The time period of small oscillations of remaining portion about `O` is -

Options

A. `3pi sqrt((R )/(g))`
B. `pi sqrt((13R)/(g))`
C. `2pi sqrt((39R)/(16g))`
D. `2pisqrt((7R)/(6g))`

Answer

B

Explanation

A uniform …………
`T = 2pi sqrt((I)/(mgy_(cm)))`
`I = (MR^(2))/(2) - ((1)/(2)(M)/(4)((R )/(2))^(2) + (M)/(4)((R )/(2))^(2))= (13MR^(2))/(32)`
`y_(cm) = (R )/(6)`
`T = 2pi sqrt((13)/(4) (R )/(g))`