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A uniform disc of mass m & radius R is p...

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 -

A

`3pi sqrt((R )/(g))`

B

`pi sqrt((13R)/(g))`

C

`2pi sqrt((39R)/(16g))`

D

`2pisqrt((7R)/(6g))`

Text Solution

Verified by Experts

The correct Answer is:
B
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))`
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