Three mass points `m_(1)m_(2)` amd `m_(3)` are located at the vertices of an equilateral triangle of length a. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through `m_(1)`?

Explanation

As shown in figure, the axis of rotation passes through `m_(1)`. The distance of `m_(1),m_(2)` and `m_(3)` from the axis of rotation are `O,a/2` and `a/2` respectively.
`:.` M.I of the system about the altitude through `m_(1)` is
`I=m_(1)r_(1)^(2)+m_(2)r_(2)^(2)+m_(3)r_(3)^(2)`
`=m_(1)(0)^(2)+m_(2)(a/2)^(2)+m_(3)(a/2)^(2)`
or `I=(a^(2))/4(m_(2)+m_(3))`