A uniform semi-circular disc of mass `m` and radius `r` is suspended as shown in the figure. If `T` is the time period of small osciallations about an axis passing through point of supension and perpendicular to plane of disk. Then `T` is equal to

Options

A. `2pisqrt((3r)/(8g))`
B. `2pisqrt((3rpi)/(8g))`
C. `2pisqrt((2rpi)/(9g))`
D. `2pisqrt((2r)/(9g))`

Explanation

`I=(mr^(2))/(2)`
`d=(4r)/(3pi)`
`T=2pisqrt((1)/(mgd))=2pisqrt((mr^(3).3pi)/(2xxmgxx4r))=2pisqrt((3rpi)/(8g))`