Three particles, each of mass m are situated at the vertices of an equilateral triangle ABC of side L figure. Find thee moment of inertia of the system about the line AX perpendicular to AB in the plane of ABC

Explanation

As is clear from Fig.
perpendicular distance of `A` from `AX = 0`
perpendicular distnace of `B` from `AX = L`
and perpendicular distance of `C` from `AX = (L)/(2)`
`:.` Moment of inertia of three particle system about `AX`
`= 0 + mL^(2) + m((L)/(2))^(2) = (5)/(4) mL^(2)`