Three point masses `m_(1), m_(2)` and `m_(3)` are located at the vertices of an equilateral triangle of side `alpha`. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through `m_(1)?`

Explanation

Since, it can be seen in the figure given below that the axis of rotation passes through `m_(1)`. The distances of `m_(1),m_(2) and m_(3)` form the axis of rotation are `0, a//2,a//2` respectively

Therefore, moment of inertia of the system about the axis 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)`
`rArr I=(a^(2))/(4)(m_(2)+m_(3))`.