Seven identical circular rings of mass 8 g and radius 2 cmare welded symmetricallyas depicted in the adjoinig figure. The moment of inertia of the given configuration about an axis that passes through P and is perpendicular to the plane is _______`xx10^(-5)kgm^(2)`

Answer

`30.08`

Explanation

M.I. about origin O
`I_(O)=MR^(2)+6[MR^(2)+M(2R)^(2)]`
`:.I_(O)=MR^(2)+30MR^(2)`
`I_(O)=32MR^(2)`
Using parallel axes theorem,
M.I. about the point P will be
`I_(P)=I_(O)+7M(3R)^(2)`
`I_(P)=31MR^(2)+63MR^(2)`
`I_(P)=94MR^(2)=94xx8xx10^(-3)`
`xx(2xx10^(-2))^(2)`
`:.I_(P)=30.08xx10^(-5)kgm^(2)`