Two particles of masses `m` and `2m` are placed at separation `L`. Find the `M.I.` about an axis passing through the center of mass and perpendicular to the line joining the point masses.

Explanation

First, locate the center of mass (`c.m`)

`x_(c.m)=(mxx0+2ml)/(m+2m)=(2L)/(3)`
`I=mx_(c.m)^(2)+2m(L-x_(c.m))^(2)`
`m((2L)/(3))^(2)+2m((L)/(3))^(2)`
`(4mL^(2))/(9)+(2mL^(2))/(9)=(2mL^(2))/(3)`