An L-shaped body having two parts of mass `1/3 kg` and `2/3` kg and length 6m each rotates about an axis passing through the centre of mass and perpendicular to its plane. Find the moment of inertia of the body (in `kg//m^(2)`) about this axis.

Answer

5

Explanation

`x_(c)=(2/3xx3+0xx3)/1=2`
`y_(C)=(1/3xx3+0xx2)/1=1`
`I_(C)+1xx(X_(C)^(2)+y_(C)^(2))=(1xx6^(2))/(3xx3) +(2xx2)/(3xx3)`
`I_(C)+1(1^(2)+2^(2))=4+8`
`I_(C)+5=12`
`I_(C)=7 kg m^(2)`