A disc is hinged such that it can freely rotate in a vertical plane about a point on its radius. If radius of disc is `'R'` , then what will be minimum time period of its simple harmonic motion ?

Options

A. `2pisqrt((R)/(g))`
B. `2pisqrt((3R)/(2g))`
C. `2pi sqrt((sqrt(2)R)/(g))`
D. `2pisqrt((R)/(2g))`

Answer

C

Explanation

For minimum time period
`x=(R)/(sqrt(2))`
`rArr T=2pi sqrt(((mR^(2))/(2)+(mR^(2))/(2))/((mgR)/(sqrt(2))))=2pisqrt((sqrt(2)R)/(g))`
`i=[(M(Rsqrt(2))^(2))/(12)+M((R)/(sqrt(2)))^(2)]xx4+mR^(2)`
`=20kgm^(2)`.
`(4M+m)g sin theta -F=(4M+m)a.`
`F.R.=I((a)/(R))`
Solving
`a=(7g)/(24)`
`F=20alemu(4M+m)g cos 30`
`muge(5)/(12sqrt(3))`
`:. mu _(m i n)=(5)/(12sqrt(3))`